Honestly, finding a wallet that has never moved a coin out 12 to 13 years ago, and also finding a way to break into such a wallet is near impossible, I cant say it's not possible, but it's very very near impossible..
I believe @OP just created a made-up story just for the sake of discussion creating a scenario where he wanted to know the reaction and point of view of every individual that read the case presented. So we can pretend to think that the case happened and @OP wanted us to suggest something about his inquiries.
And if somehow, you manage to gain access into the wallet, to know if moving the fund is stealing or not, we have to find out what stealing truly is..
Here is what the dictionary say stealing is "To take illegally, or without the owner's permission, something owned by someone else."....
So definitely, moving the funds is stealing, as long as you don't have permission from the real owner of the wallet to do so.
The thing is, the case provided by @OP is different, it is about a lost privatekey and it is all about someone who happen to stumble on an old private key that is loitering around and there is no way to return the said items to the owner, obviously, any Bitcoin address that is not linked to any centralized services is anonymous. So as I stated in my first reply[1] on this thread, he can acquire ownership or rights on that lost private key with funds if he did the necessary procedure but the owner failed to claim the lost item.
And again, finding the true owner of a wallet, most especially, when the person already lost his or her private keys, is another near impossible thing to do,
True that but why so serious about the possibility or impossibility of the given case, I believe this is just a case study and the example is just a made-up scenario.
so if you gain access to someones wallet who already lost his or her private keys, you have no choice but to move the funds, but consider yourself as a thief already..
But just incase you don't wanna steal, or be tempted to, then stay away from snooping on people's wallet.
Stealing one's property is against the law and immoral but if you happen to stumble on an item whose owner is unknown and there is no chance to return that item, there are laws provided for that scenario where the person who finds it can have the legal right to own that lost item or property. Obviously it has to undergo certain procedures, time frames, and the failure of the owner to claim the lost item.
As stated by the common law[2], the founder can keep the item until the owner comes and claim it. He can keep but he cannot spend or move it
but the Modern interpretation of the law where many jurisdictions have statutes that modify the common law's treatment of lost property states that:
Modern Interpretations
Many jurisdictions have statutes that modify the common law's treatment of lost property. Typically, these statutes require lost personal property to be turned over to a government official, and that if the property is not claimed within a set period of time, it goes to the finder, and the original owner's rights to the property are terminated.
[1]
https://bitcointalksearch.org/topic/m.62059069[2]
https://www.law.cornell.edu/wex/statute