IF they still have the private key, they should just move the funds the moment they realize a copy is missing.
That should happen likely but would leave @easternklaas as apparently honest finder with empty pockets unless the legit owner shows some gratitude to the honest finder.
I find this line of thinking a bit odd. If one goes about his life ethically, there shouldn't be any expectation of reward for doing the right thing. Honesty and integrity are rewarding enough for those that value such attributes. As honest as easternklaas has been, he's not
entitled to anything, and it's comforting that he seems to realize that.
I like suchmoon's analogy: If you find a key to someone's house on the street, or along the same lines; a username and password for a bank account, that doesn't entitle you to any of their furniture or a portion of the funds in the account. This is no different.