What if i catched some mot****er, who is using one of my wallets - how can i prove that it's mine?

I don't understand who you would need to prove it to, but if you are the owner and someone is using your wallet, there are two scenarios: either they have withdrawn all of your funds, and therefore you essentially cannot prove anything, or if they have only moved a few funds, you need to quickly move all of them before it's too late. There's no need to prove anything to anyone; otherwise, what's the point of anonymity?