I'm not sure what you mean by the Lost and Found office? Sounds like a hotel or some other venue. Besides registering the camera gear with the police, did you also turn it over physically to the police? I'm not sure how a lost and found department of a business can actually grant ownership of something like this to someone in such a short time (30 days) without it being held by the police so they can determine if it was stolen - a possible scenario.
I lost a bag full of photo gear one time when I left my bag beside my car at a hotel and drove off - yes...stupid, but it happened. Several hundred miles later when I realized, I went back, but of course everything was gone. Nobody at the hotel knew anything, so I reported it to the police. Fortunately I had written down all the serial numbers just the week before, so when I got home from my trip I called the officer who was working the case and gave him the numbers. That was it. I had to buy all new gear. I figured it was case closed.
Nine months later I got a phone call from the same officer. He indicated that one of the serial numbers from my gear turned up in a pawn shop in a neighboring state over 500 miles away. He told me to stay put, but it looked like maybe I'd get some of my stuff back. This officer was over 500 miles away from where some of my gear turned up. But, when some serial numbers matched a list of stolen property which was in a multi-state database, it triggered an alert, which eventually led to him knowing about it. He contacted the local police in the area where the item was pawned, and they went from there. It was still legally my property, BTW. I never gave up my rights to it because I lost it. In conclusion, the local police were able to trace the pawned items to a person of interest. When they interviewed him, he came clean and produced the rest of the gear, minus a few rolls of film and other small things. Even a small point/shoot camera was still in my bag. The guy said he bought it from someone, later said he found it, didn't know it was "stolen." Once the stuff was in the possession of the police, I was told I could come claim my property. I had to produce some meaningful documents, but mainly I had to identify myself. I signed a few things, and they turned it back over to me. They gave me a release document for the pawn shop so I could retrieve the items that had been pawned (which triggered the whole recovery process in the first place.) Total time from when first notified about it to recovery -- about three weeks and 200 miles travel to neighboring state. Sometimes, the system does work.
In your case, you turned the stuff in to someone (lost and found,) but it just seems to me that they awarded it to you rather quickly, and the real owner still could turn up down the line. What then?
Don't mean to rain on your parade, seriously. But that's some expensive gear for someone to simply walk away from. Something seems out of place here...