He took on Petes identity but not Petes personality
Even though he knew Pete's family hadn't seen him in 20 years and he was passable for what Pete probably looks like today, he didn't act like Pete at all. I would have thought he would have taken on some of the goofball, doofus characteristics the real Pete had so as to have a better cover and make himself more believable.
" Tell me mom...when your little girl's on the slab...where will it tickle you?"