Judgment, Supreme Court, New York County (Richard D. Carruthers, J.), rendered May 11, 2007, convicting defendant, after a jury trial, of assault in the first degree and criminal possession of a weapon in the second and third degrees, and sentencing him, as a persistent felony offender, to concurrent terms of 20 years to life on each count, unanimously affirmed.
The court properly exercised its discretion in receiving police testimony that the victim named defendant as his assailant immediately after the crime. These prior consistent statements were admissible to rebut a claim of recent fabrication. A major component of defendant’s trial strategy was to attack the victim’s credibility by arguing that he was motivated to testify falsely by a cooperation agreement, entered into more than a year after the shooting, which required him to testify against defendant in exchange for a lenient sentence in his own drug case. The prior consistent statements clearly predated that particular motive to falsify. Defendant’s trial strategy also included a theory that the victim had deliberately misidentified defendant at the outset of the case, in order to avoid revealing that the shooting involved the victim’s own drug trafficking. However, there is no requirement that, to be admissible, a prior consistent statement predate all possible motives to falsify (see People v McClean, 69 NY2d 426, 430 [1987]; People v Baker, 23 NY2d *525307, 322-323 [1968]). We also note that the court’s limiting instructions were sufficient to prevent any undue prejudice. In any event, any error in receipt of this testimony was harmless in view of the overwhelming evidence against defendant. Among other things, there were recorded conversations in which defendant not only displayed a consciousness of guilt but virtually admitted the crime.
The court also properly exercised its discretion in receiving evidence that while the victim was incarcerated on his own case, an unnamed inmate threatened him with harm if he testified against defendant. The jury could have reasonably inferred, from all the circumstances, that it was unlikely that such a threat would have been made without defendant’s instigation or authorization (see People v Cotto, 222 AD2d 345, 345 [1995], lv denied 88 NY2d 846 [1996]). The court provided appropriate limiting instructions. Any error was harmless both because the evidence of guilt was overwhelming, and because the testimony at issue was cumulative to other consciousness-of-guilt evidence that was much more damaging.
Defendant’s challenge to the constitutionality of his sentencing as a persistent felony offender is unavailing (see People v Battles, 16 NY3d 54 [2010]; People v Quinones, 12 NY3d 116 [2009]). Concur—Tom, J.P., Mazzarelli, Acosta, Renwick and Freedman, JJ.