I am sorry this cat is yours now!!!! If they left it, they neglected it and that is cruelty to animals and a large fine or prison sentence would ensue.

You would have evidence on your side. vet records that you have cared for it.

The girlfriends mum could prove when she moved into the hosue. Their passport would show when they left the country. The law would be on your side my friend.

If any vet would consider not backing you up that you have nutured this cat back to health then they are in the wrong job!!