*533SUMMARY ORDER
Defendant-appellant Christopher Thomas appeals a June 19, 2003 judgment of the United States District Court for the Eastern District of New York (Gleeson, J.) sentencing him to 115 months imprisonment and three years of supervised release, and requiring him to pay $200,000 in restitution, following his plea of guilty to eight counts of wire fraud in violation of 18 U.S.C. § 1343 and one count of conspiracy to commit wire fraud in violation of 18 U.S.C. § 371. We assume the parties’ familiarity with the underlying facts and procedural history.
In the brief filed by his new appellate counsel, Thomas contends that he was denied the right to conflict-free representation because the United States Attorney’s Office that was prosecuting him may at the same time have been investigating his defense attorney, John H. Jacobs. See Armienti v. United States, 234 F.3d 820, 824 (2d Cir.2000) (stating that an “actual” conflict of interest exists when “during the course of the representation, the attorney’s and defendant’s interests diverge with respect to a material factual or legal issue or to a course of action” (internal quotation marks omitted)). Thomas contends that Jacobs may have withdrawn a potentially meritorious argument, regarding the amount of loss involved in the conspiracy, to earn favorable treatment from the prosecutors in his own case. See id. (requiring a defendant claiming the existence of an actual conflict of interest to demonstrate a “plausible alternative defense strategy” that was “not undertaken due to the attorney’s other loyalties or interests” (internal quotation marks omitted)). We agree with the parties that adjudication of Thomas’s conflict of interest claim requires further factfinding. Because Thomas already has pending before the district court a motion pursuant to 28 U.S.C. § 2255 that includes ineffective assistance of counsel claims regarding Jacobs’s representation, we dismiss Thomas’s conflict of interest claim here without prejudice to his amending his § 2255 motion to include it. See United States v. Oladimeji, 463 F.3d 152, 154 (2d Cir.2006) (“Where the record on appeal does not include the facts necessary to adjudicate a claim of ineffective assistance of counsel, our usual practice is not to consider the claim on the direct appeal, but to leave it to the defendant to raise the claims on a petition for habeas corpus under 28 U.S.C. § 2255.”). Because the district court has not yet “adjudicated] on the merits” Thomas’s § 2255 motion, a motion to amend would not be treated as a successive petition, but rather would be governed by Federal Rule of Civil Procedure 15(a), which requires that leave be “freely given.” Littlejohn v. Artuz, 271 F.3d 360, 363 (2d Cir.2001).1
Thomas’s original appellate brief, filed on his behalf by Jacobs, raises two additional arguments. First, Thomas contends that he was denied the right to make a statement before the imposition of sentence as required by Federal Rule of Criminal Procedure 32(i)(4)(A)(ii), which directs the district court to “address the defendant personally in order to permit the defendant to speak or present any information to mitigate the sentence.” See United States v. Li, 115 F.3d 125, 132-33 (2d Cir.1997) (stating that although the right to allocute is not a constitutional guarantee, it is an “absolute right in the federal courts” (internal quotation marks omitted)). Thomas had ample opportunity *534to make a statement and present information to mitigate his sentence, however, and was not denied his Rule 32 right. After accepting Thomas’s guilty plea at the August 16, 2002 hearing, then-District Court Judge Reena Raggi instructed Thomas to “think about what you want me to know about [your recidivism] between now and sentencing.” In his February 28, 2003 letter to Judge Raggi, Thomas indicated he was writing pursuant to “Rule 32(c)(3)(C),” which we take as a reference to the provision now codified as Rule 32 (i) (4) (A) (ii). See United States v. Margiotti, 85 F.3d 100, 103 (2d Cir.1996) (quoting former Federal Rule of Criminal Procedure 32(c)(3)(C) for the rule now found at 32 (i) (4) (A) (ii)). In this letter, Thomas discussed “facts [that he] believe[d] mitigate the sentence to be imposed,” explained his reasons for “revert[ing] back to criminal behavior after having served a considerable period of incarceration,” and described his participation in a counseling program that had “enabled [him] to better appreciate the need to be responsible for [his] misconduct.” Judge John Gleeson, to whom the case was reassigned, discussed the letter with Thomas during the June 19, 2003 sentencing hearing. Prior to imposing sentence, Judge Gleeson also asked Thomas whether he had “anything further” to add, to which Thomas, who by his own admission had prior experience with sentencing, responded in the negative. Thus, Thomas had a full opportunity to make a statement and present mitigating information.
Second, Thomas contends that Judge Gleeson erred when he denied Thomas a two-point reduction under the Sentencing Guidelines for acceptance of responsibility based on Thomas’s February 28, 2003 letter to Judge Raggi, in which Thomas sought to mitigate his punishment. Even if we were to accept Thomas’s contention that Judge Raggi’s statement that she would accept no further pro se submissions was a ruling subject to the law-of-the-case doctrine, Judge Gleeson simply would not be precluded from revisiting that sua sponte ruling. See generally Official Comm, of Unsecured Creditors of Color Tile, Inc. v. Coopers & Lybrand, LLP, 322 F.3d 147,167 (2d Cir.2003).
Finally, we find no merit in the arguments contained in Thomas’s pro se appellate briefs. First, Thomas, argues that the district court erred in accepting his guilty plea because an adequate factual basis for the plea was lacking. See Fed. R.Crim.P. 11(b)(3). Contrary to Thomas’s contention, however, a conspiracy under 18 U.S.C. § 371 to violate 18 U.S.C. § 1343 does not require an agreement to devise a scheme or artifice to defraud. Section 371 requires only “an agreement between two or more persons to commit a specified federal offense,” United States v. Snype, 441 F.3d 119, 142 (2d Cir.2006), and § 1343, the “specified federal offense” here, requires only, to the extent pertinent, proof of “the existence of a scheme to defraud,” United States v. Autuori, 212 F.3d 105, 115 (2d Cir.2000) (emphasis added). Moreover, the government’s proffer and Thomas’s allocution were sufficient to establish a factual basis for the plea as to the telephone calls and computer transmissions involved. Second, our decision in United States v. Roque, 421 F.3d 118 (2d Cir.2005), forecloses Thomas’s claim that his guilty plea was involuntary because he made it on the mistaken assumption that the Sentencing Guidelines would remain mandatory. Id. at 124. Third, Thomas’s claim that he should not have received a leadership sentencing enhancement is without merit because it depends on his mistaken belief that a conspiracy to violate 18 U.S.C. § 1343 requires that the conspirators collectively devise the scheme to de*535fraud. Fourth, Judge Gleeson did not err in finding that the statements in Thomas’s February 28, 2003 letter were false, particularly given that Thomas did not dispute that finding and instead attempted to withdraw the letter. Finally, despite Thomas’s contention to the contrary, the restitution ordered by the district court did not exceed the amount of loss the government asserted, and Thomas’s counsel conceded, that the victim had suffered. We do not reach Thomas’s additional claim that the district court overstated the amount of loss in applying U.S.S.G. § 2X1.1, because Thomas’s new appellate counsel asserts that attorney Jacobs may have abandoned this claim prior to sentencing to curry favor with prosecutors, and thus its merits will be considered along with the conflict of interest claim in the context of Thomas’s § 2255 motion.
The parties do not dispute that Thomas is entitled to a remand under Crosby for the limited purpose of determining whether he should be resentenced in light of the Supreme Court’s holding that the Sentencing Guidelines are non-mandatory. Crosby, 397 F.3d at 117. Because Thomas’s direct appeal was pending when the Supreme Court decided United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), we agree that a Crosby remand is appropriate.
For the foregoing reasons, we AFFIRM the judgment of conviction and REMAND for further sentencing proceedings pursuant to Crosby.
. The government at oral argument has represented to the Court that it will not oppose, on the ground of untimeliness, the defendant’s motion to amend the habeas petition to add this claim of ineffectiveness of counsel.