When you find a stray cat, the first thing you must do is check for a collar and microchip.
If the cat has no identification, look online. You can check lost pet pages on Facebook, Nextdoor, and Craigslist. You can also post on these sites that you have found a stray cat.
Warning: do not believe everyone who claims the cat. Tell them they must provide a photo of the cat, or a feature only the owner would know, that you did not disclose in your listing...