Although I'm open to psychic communication; when I began the thread, I meant the type of detective who goes round physically looking for the cat. For example, AnimalUk knock on doors, search sheds, give out leaflets, put posters on lamp-posts, and their uniforms, ID, and professional manner mean that they're taken far more seriously than your average me. People treat them like the RSPCA.
Hence any cat nabbers are frightened into releasing said cat.
Pebbles isn't a candidate for theft. He's a moggy, doesn't like being handled, and neutered. I did wonder if one of the incoming students had felt homesick and taken him in, but they would be more like to 'adopt' a friendly cat than one who runs away if you try to stroke him!
I don't know if anyone remembers the problems I had with a neighbour when I took in Lucy and her flu-ridden kittens. She claimed that she 'owned' Lucy (a long time feral who had her kittens in my verandah one November). It has crossed my mind that, being aware that I'm moving soon, she's stolen Pebbles in error, thinking this was Lucy, (who she called Dotty: she names the local ferals, but doesn't give them a home). In this case a pet detective of the AnimalUk type could be useful. Pebbles is microchipped.
A friend's daughter is psychic re cats and has said that she thinks Pebbles is fine and close by. But I need more practical help than this as I'm preparing to move house and dreading leaving him behind.