This is terrible - you must feel horrified and ashamed.
However, I did just want to add that my own DSS did something very similar to this, when he was just a little younger than yours. Startlingly similar in fact (I can't go into any more details).
Well over a decade on, he is now one of the most sweet, altruistic, loving people I know, and even tho I am no longer with his dad, DSS and his lovely partner remain two of the first people I can turn to in any crisis.
The key is, I think, to understand what is behind it. Why has he done it? If it is simply desire for money, and he just doesn't care on way or another about his nan, then yes that is almost psychopathic. But often there is much more to it. Is he being threatened by someone? Scared, possibly? Would his girlfriend have known about this and been getting involved?
Please think very carefully about telling the police. Well frankly I just wouldn't do it, ever, to a member of my family. Not over a theft (however callous and disgusting, as I agree this is).
As for cancelling Christmas - his gifts, certainly, should be returned and the money used to pay back as much as possible of what he owes.
I do think, however, that ostracizing him would be a potentially disastrous choice at this time, in terms of his future outcomes. As we learnt with my stepson, these were the times when he actually needed the most love from us. (And yes, it was very hard to show it). When it all came out what he had done, the shame was very very intense (tho he masked it with anger, self-medicated it with booze and drugs, etc) - we actually became quite scared that he would seriously harm, even kill, himself in the depths of his self-loathing and despair. He still to this day sometimes requires reassurance from his sister's and I that we don't still hate him for it.
So if you can force yourself to, I would try to spend time with DSS. Show him that you still love him and that in time you will forgive him, once he has done everything in his power to put this right. He needs more than anything to believe that change is possible.
Good luck. So sorry this has happened. And sending all best wishes for the health of your poor DMIL, who sounds like a lovely, trusting person.