Gustavo Monteon-Camargo, a native and citizen of Mexico, petitions for review of a final order of removal by the Board of Immigration Appeals ("BIA" or "Board"). The BIA determined that Monteon-Camargo was ineligible for cancellation of removal because his 2007 conviction of attempted theft from a person under Texas law counts as a crime involving moral turpitude ("CIMT") under a 2016 BIA decision. We grant the petition and reverse and remand because that retroactive application was error.

I.

Monteon-Camargo first entered the United States in 1998 on a non-immigrant visa but was arrested and administratively returned to Mexico in 2004. He reentered on an unknown date and was arrested by the Department of Homeland Security ("DHS") in 2010. DHS served him with a Notice to Appear, charging him with inadmissibility as an alien present in the United States without being admitted or paroled, in violation of 8 U.S.C. § 1182 (a)(6)(A)(i).

During removal proceedings, Monteon-Camargo submitted an "Application for Cancellation of Removal and Adjustment of Status for Certain Non-permanent Residents." DHS submitted a judgment showing that in 2007, Monteon-Camargo had pleaded guilty of attempted theft from a person in violation of Texas Penal Code § 31.03. 1 Deciding that that offense was a CIMT and that Monteon-Camargo thus had failed to establish one of the prerequisites for eligibility for cancellation of removal-that his conviction was not a CIMT-the immigration judge ("IJ")

*427 found Monteon-Camargo removable as charged. 2

Monteon-Camargo appealed to the BIA, contending that the IJ erred in failing to apply the modified categorical approach to determine whether the attempted-theft conviction was a CIMT. He asked the BIA to remand to allow him to supplement the record with his conviction records so he could show that his conviction was not a CIMT. 3

The BIA dismissed the appeal. It agreed with the IJ that attempted theft from a person under § 31.03 is categorically a CIMT and that Monteon-Camargo was therefore statutorily ineligible for cancellation of removal. The Board based its decision on In re Diaz-Lizarraga , 26 I. & N. Dec. 847 , 848 (BIA 2016), which announced that a theft offense is a CIMT if it involves a taking or exercise of control over another's property without consent and with an intent to deprive the owner of his property either permanently or under circumstances in which the owner's property rights are substantially eroded. A defendant could not be convicted of violating § 31.03, the BIA continued, unless his conduct met the definition in Diaz-Lizarraga . The BIA also noted that Texas caselaw confirms "that a theft conviction may not lawfully be entered absent proof beyond a reasonable doubt that the accused intended permanently to deprive the victim of the value of his property." Consequently, the Board concluded, Monteon-Camargo's conviction is a CIMT. 4

While his petition for review to this court was pending, Monteon-Camargo moved the Board to reopen and reconsider its decision dismissing his original appeal of the IJ's decision. The BIA denied that motion, whereupon Monteon-Camargo filed a second petition for review in this court. We consolidated the two petitions, and the parties filed supplemental briefing.

After that, several of our sister circuits held that the Board may not retroactively apply Diaz-Lizarraga 's definition of CIMTs to predicate offenses committed before that decision. 5 Monteon-Camargo and the government have submitted several supplemental letters addressing those cases.

II.

We review the BIA's rulings of *428 law de novo , "giv[ing] Chevron deference ^[ 6 ^] to the BIA's interpretation of the term 'moral turpitude' and its guidance on the general categories of offenses which constitute CIMTs." Laryea v. Sessions , 871 F.3d 337 , 341 (5th Cir. 2017) (internal alterations and citation omitted). Because the BIA agreed with the IJ's rulings, we review the decisions of both the BIA and the IJ. See Zhu v. Gonzales , 493 F.3d 588 , 593 (5th Cir. 2007).

An alien is eligible for cancellation of removal if, among other things, he "has not been convicted of an offense under section 1182(a)(2)" 7 -that is, "a [CIMT]." 8 U.S.C. § 1182 (a)(2)(A)(i)(I). The alien has the burden to establish eligibility for cancellation of removal. Id. § 1229a(c)(4)(A). Put differently, the alien must prove that his conviction was not a CIMT.

Congress did not define "moral turpitude" in the Immigration and Nationality Act but "left the interpretation of this provision to the BIA and interpretation of its application to state and federal laws to the federal courts." Rodriguez-Castro v. Gonzales , 427 F.3d 316 , 319-20 (5th Cir. 2005). The BIA has long maintained that "theft [is] ... a [CIMT]," Okoro v. INS , 125 F.3d 920 , 926 (5th Cir. 1997), and this court has consistently deferred to that holding. See id.

Historically, the BIA has held that a theft offense is categorically a CIMT only if it was "committed with the intent to permanently deprive an owner of property." 8 But the BIA altered its position in 2016. In Diaz-Lizarraga , a formal adjudication, the BIA opined that "lawmakers and judges across the country have come to recognize that many temporary takings are as culpable as permanent ones." Diaz-Lizarraga , 26 I. & N. Dec. at 851 . The Board thus revised its interpretation of which theft crimes constitute CIMTs, holding "that a taking or exercise of control over another's property without consent ... is a [CIMT] if it involves an intent to deprive the owner of his property either permanently or under circumstances where the owner's property rights are substantially eroded." Id . at 852-53 (some emphasis added).

The BIA applied that new standard to classify Monteon-Camargo's conviction as a CIMT. Monteon-Camargo contends that the BIA's retroactive application of Diaz-Lizarraga violates due process. But before we reach the merits of that argument, we must decide two threshold questions: whether he waived the issue and whether we have jurisdiction.

A.

"Generally speaking, a [party] waives an issue if he fails to adequately brief it." United States v. Martinez , 263 F.3d 436 , 438 (5th Cir. 2001). That "rule is a prudential construct that requires the exercise of discretion." Id. (internal quotation marks and citation omitted). Federal Rule of Appellate Procedure 28(a)(8)(A) instructs a party to brief his "contentions and the reasons for them, with citations to the authorities and parts of the record on which the [party] relies." Still, this court has the discretion to consider inadequately briefed claims and has done so. See, e.g. , Martinez , 263 F.3d at 438 .

Monteon-Camargo first contended that the BIA erred in retroactively applying *429 Diaz-Lizarraga in his supplemental brief, devoting just over a page to the theory and citing no authorities. But both parties have filed supplemental letters addressing the issue and providing authorities.

Despite the sparse briefing, we exercise our discretion to consider Monteon-Camargo's retroactivity claim. Three of our sister circuits have held that the BIA's revised CIMT definition may not be retroactively applied to predicate offenses committed before Diaz-Lizarraga was issued. 9 We are also satisfied that the parties have adequately presented their positions in the supplemental letters, making it appropriate to decide the issue.

B.

The government contends that we do not have jurisdiction to decide Monteon-Camargo's retroactivity claim, averring that judicial review is unavailable under § 1252(d)(1) because Monteon-Camargo did not present that claim to the BIA. 10 "Judicial review of a final removal order is only available if 'the alien has exhausted all administrative remedies available to the alien as of right.' " Vazquez v. Sessions , 885 F.3d 862 , 868 (5th Cir. 2018) (quoting 8 U.S.C. § 1252 (d)(1) ). That exhaustion requirement is "mandatory and jurisdictional." Omari v. Holder , 562 F.3d 314 , 324 (5th Cir. 2009) (emphasis omitted). "An alien fails to exhaust his administrative remedies with respect to an issue when the issue is not raised in the first instance before the BIA." Vazquez , 885 F.3d at 868 (internal quotation marks, alteration, and citation omitted). "[T]o satisfy the exhaustion requirement ... a petitioner must 'raise,' 'present,' or 'mention' an issue to the BIA" in his brief to the Board. Id. (citing Omari , 562 F.3d at 321 ).

Due process claims, however, are generally exempt from the exhaustion doctrine because they are not within the purview of the BIA. Anwar v. INS , 116 F.3d 140 , 144 n.4 (5th Cir. 1997) (citations omitted). "[W]hen a petitioner's due process claim does not assert a procedural error correctable by the BIA, it is not subject to an exhaustion requirement." Lopez De Jesus v. INS , 312 F.3d 155 , 162 n.47 (5th Cir. 2002).

Monteon-Camargo raises a due process challenge to the BIA's decision, *430 contending that Diaz-Lizarraga cannot apply retroactively because of "the due process interests of fair notice." The government counters that retroactivity claims are not per se constitutional due process claims that the BIA is unable to correct. And Monteon-Camargo, the government suggests, is alleging "procedural error," Falek v. Gonzales , 475 F.3d 285 , 289-90 (5th Cir. 2007) (internal quotation marks and citation omitted), because his "supplemental brief does not mention the [C]onstitution, let alone establish that [his retroactivity claim] is the type of argument that the Board is unable to review." The government concludes that under Falek , Monteon-Camargo needed to exhaust his retroactivity claim before the Board.

But unlike in Falek , id. , Monteon-Camargo presses a constitutional claim, contending that retroactively applying Diaz-Lizarraga compromises his " 'due process interests in fair notice, reasonable reliance, and settled expectations' " (quoting De Niz Robles v. Lynch , 803 F.3d 1165 , 1169 (10th Cir. 2015) (Gorsuch, J.) ). 11 Accordingly, his retroactivity claim "is not subject to an exhaustion requirement," Lopez De Jesus , 312 F.3d at 162 n.47, and we have jurisdiction to consider it.

C.

That takes us to the merits. "[T]he leading case on administrative retroactivity" instructs that any disadvantages from the " 'retroactive effect[s]' " of deciding a " 'case of first impression ... must be balanced against the mischief of producing a result which is contrary to a statutory design or to legal and equitable principles.' " Microcomputer Tech. Inst. v. Riley , 139 F.3d 1044 , 1050 (5th Cir. 1998) (quoting SEC v. Chenery Corp ., 332 U.S. 194 , 203, 67 S.Ct. 1760 , 91 L.Ed. 1995 (1947) ). To apply that instruction, this court "balance[s] the ills of retroactivity against the disadvantages of prospectivity." Id . 12 "If that mischief [of prospectivity] is greater than the ill effect of the retroactive application of a new standard, it is not the type of retroactivity which is condemned by law." Chenery , 332 U.S. at 203 , 67 S.Ct. 1760 . We must thus balance the ills of applying the BIA's new interpretation of which thefts constitute CIMTs against the disadvantages of applying the change solely to predicate offenses adjudicated after Diaz-Lizarraga .

Because the retroactivity issue was first raised in the supplemental briefing, the various briefs say little about the disadvantages of retroactivity versus prospectivity. There are, however, some obvious disadvantages. Criminal defendants may have pleaded guilty of crimes that they rightly thought, based on the Board's prior position, did not constitute CIMTs. Accordingly, they may have entered pleas believing that they would not suffer adverse immigration consequences as a result. Retroactively applying Diaz-Lizarraga thus would compromise the "familiar [due process] considerations of fair notice, *431 reasonable reliance, and settled expectations." Landgraf v. USI FilmProds. , 511 U.S. 244 , 270, 114 S.Ct. 1483 , 128 L.Ed.2d 229 (1994).

The change in the Board's guidance, moreover, was significant: It added an entirely new category of theft offenses to those considered CIMTs. In Diaz-Lizarraga , the Board recognized that it was drastically changing the landscape, observing that it was "updat[ing]" what had been its position "[f]rom [its] earliest days." Diaz-Lizarraga , 26 I. & N. Dec. at 849, 852 . Applying such a broad "new rule[ ] of general applicability" to prior conduct contravenes basic presumptions about our legislative system. De Niz Robles , 803 F.3d at 1169 . A "presumption of prospectivity attaches to Congress's own work," and it should generally attach when an agency "exercise[s] delegated legislative ... authority." Id. at 1171-72 .

Though there are multiple disadvantages to applying it retroactively, the government has not identified a single disadvantage of applying Diaz-Lizarraga only prospectively. We conclude that the definition of CIMTs announced in Diaz-Lizarraga may be applied only to crimes committed after that decision issued. The BIA erred in applying its new definition to Monteon-Camargo's conviction of attempted theft.

The petition for review is GRANTED. The order is REVERSED and REMANDED for further proceedings. 13