Regardless of his ugliness and her golddigging nature, the issue here is a breach of contract (engagement broken). No marriage, no ring, sluts.
I realize, she is in the wrong and needs to return the ring. Still, he is an idiot. But love is blind.... so is lust.
An engagement ring is a gift, not compensation in a contract. Accepting a gift does not constitute a contract.
This is actually a common case presented in the first contract Law, or Business course. It has been ruled on, and is well established in case law.
A contract requires both parties to agree to a contract, that there be substantial compensation, and that it be for a lawful purpose.
Marrying for money is not technically a lawful purpose (prostitution).
Since this guy is loaded, his lawyers will pursue whatever (within reason) he wants them to pursue. The lawyers could certainly badger and harass his ex for him, but he really has no right to insist on the return of the ring.
I have to agree with youb if he had broken off the engagement then she could keep itb but she broke the contract and should return it.
It’ll cost him more to get it back than it’s worth.