I think this argument could go a million of different ways. I think there are legal arguments for both sides. If it was "misplaced" the rightful owner would get it (in this case rightful ownership transferred to GW). If it is abandoned, it is fair game (legally, not morally). Something on the floor is a bit more obvious of being abandoned while finding a wallet in a restaurant booth is most certainly not abandoned. In this case the quirk comes in the fact that the jacket was donated. Can an owner abandon something they do not even know exists in their item? I don't know the answer to that. It seems that we all agree that if there is something else in what is found that is actually chattel (like a diamond ring in a purse), than the ring should be handed over to GW. Money is no different, even if the law is on your side.
This is definitely a moral question then, and I think the fair thing to do is to buy the jacket. The aforementioned discussion of leaving the jacket to be mated or for someone else doesn't really fly because the jacket can be re-donated minutes later.
Bottom line: Legally I think it would be successfully argued that you found abandoned property. However, the thrift gods may place a dry spell in your future.