You can't.

In the scenario where you both know one or more private keys from the wallet, but only you know the seed phrase, then it is possible to prove that you are the real owner of the wallet by providing a proof (ideally, a zero-knowledge proof) that you are in possession of the seed phrase which was used to derive those private keys, while the other party is not.

In the scenario where you both know the seed phrase, there is no way to prove who was the original creator of that seed phrase.