[Mr Chips]

Red, I just remembered the other thing that I was going to mention. Modern openers have rolling frequencies, and they will not work until synch'd with the opener itself. Check your manual, but I believe that you will find that you can "cleanse" the opener, so that none of your remotes work, and can then reprogram the remotes that you do have to work, which should render the stolen one useless.

That's correct of most openers made from around 1997 and on. If your opener is older, it might be time to go shopping