Sorry - -I thought that last post was a statement of intent, not that you were asking for opinions. You may or may not be able to insist on repayment.
He and his mother are obviously going to deny it until they're blue in the face, and at the moment you know it is him, but you can't prove it, IFSWIM.
I think if he is caught on camera their stance will be:
a) This is the first time he's done it - he was so hurt that you accused hm that he thought he might as well be a thief as be thought a thief.
b) He needed cash and "borrowed" some. He would have asked but he knows that you hate him and wouldn't give him it. He was going to put it back
c) You deliberately left cash/cards available to tempt him as you knew he was short of money
I really think you're "damned if you do, damned if you don't" try to make him pay it back. I can't see how you could force the issue. But you definitely ned to call the police.
His mother, who should be emotionally supporting him is letting him behave badly because it suits her. This isn't parenting - parenting is taking the hard option when necessary for the good of the child. She both wants to be the favourite parent and get back at her ex and you.
I can't see things ending well for this boy, especially if she has a new bloke on the scene and she starts to find her so a drag.
All you can do is make sure he knows he is welcome in your home as long as he behaves appropriately - i.e. no thieving or going into any bedroom other than his own for any reason; private rooms are just that - private.