Hi Robin. This is a good question. First of all we would use 'a' in this context. Because 'a' is the indefinite article. If you use 'a' it does not define who the wallet belongs too. We would use 'my' (personal pronoun).... "Have you found my wallet"? "Have you seen my wallet"? "Have you got my wallet"? I hope this helps.

Thanks Matthew!

I would say, "Have you found my wallet?" Asking "Have you got my wallet?" sounds rude to me.