He had eight children (in exile in England), but none of them had heirs.
So we do it British style, go up the family tree and find the nearest cousin or whatever.
You die without an heir, your property reverts to the state. Looks like the diamond is already with its true owner.
The British crown is the legal owner now, so bringing the law into it doesn't help you. It's not a legal matter it's a moral one, and OP made a very good point about why that's more difficult than you might think.