This is a miserable act and quite apart from the betrayal of family trust, it may be an indication that he is in deep financial trouble, possibly even more than you realise. I think you need to sit down with him and have a serious discussion because he may have got himself involved with drugs as well and be stealing to fund a habit. I don't know how old your son is but whatever his age, I think he needs to be marched round to your mother, made to apologise, and forced to repay the money. Whether you report it to the police is up to you and your mother but if she doesn't want to prefer charges, you might be able to have a word with them informally so that they pay him a visit and put the frighteners on him. And please be sure you lock up your valuables and documentation and carry your own credit card & money with you at all times, even if you have to carry in a a bum bag round your waist.
Frankly I think your son probably needs a hard shock to jolt him into understanding the consequences of his action, and a police prosecution might jolt him sufficiently to halt his early criminal career in its tracks. If you don't stamp on him now he'll probably slide further down the slippery slope.