I agree with avoiding contact with the thief -- it's tempting to try some advanced tech solution, but lots can go wrong, including accusing innocent people.

Have you talked to the hotel staff? I'm sure theft is something they are used to dealing with. If no response from them, maybe you could call the hotel corporate HQ. It's a long shot, but maybe the hotel can reimburse through insurance. Also if you have a credit card sometimes they will provide limited travel insurance.