When Carly checks on Pete's identity in the Bridgeport Police database, he is marked as arrested on 3/25/12 and convicted on 4/15/12 while the real Pete Murphy is marked as arrested on 7/12/12 and convicted on 8/29/12. Even in Stalin-era USSR or Star Trek's Cardassian empire no one can be arrested, tried and convicted in a few weeks' time.