Cat came back but looks different

I lost my cat Pax about 3 weeks ago and I posted all over about him. Today, my neighbor texted me saying she had a cat that looked and acted similar to Pax. I came over and it looks so much like him down to his fur pattern. He’s neutered like my cat was, and was very vocal and friendly like him too. I’m so convinced it’s him except for one thing: his jaw looks busted up. Idk what could’ve possibly happened to him. I’m going to give him a bath and take him to the vet but if anyone has any suggestions as to what could’ve happened or if they’ve seen this before, please let me know. That’s the only thing keeping me from fully believing this is my cat. The first pic is him currently and the last 3 pics are him before he went missing. (I know it looks like I’m squishing his face but I’m being very gentle)