Its a difficult one - obviousley i dont know your son.
Firstly is it possible your mum has got confused about your son visiting or the carer misheard her and that was a referral too the past rather than recently.? or did the carer see your son herself.
If he cant touch her money are there other valuables he could take and if so could you get a small safe or lock up box to put them in - or is it possible that he visited because he genuinley has affection for her and doesnt soley see her as a source of cash. Maybe because he feels remorseful about the way he has treated them before your dad died, In which case then if you keep your and her posessions, that he may be able to cash in, safe, is it so bad if he does visit and your mum doesnt feel the need to lie about it.
Obviousely its a major concern if he is violent toward her or you think he might be if he has no way to get his hands on her stuff, but if he cant take her stuff then either the visits will subside or he will be company for her - if she is aware of what he has done and forgiven him and he cant repeat it then it sugests remorse or at least genuine affection for her and maybe she could be instrumental in helping him in other ways that are actually helpful -
Does your son have a gambling addiction in which case is there any way you or she can persuade him to get professional help and move on from it, so you too can start to forgive his past behaviour, which surely would be better all round for everyone in the end ?
After that i,m stuck -but if you really are worried that he has been round and may be going round again behind your back and that his intentions are bad, then maybe you could get cctv - not on what is said inside the house because thats very invasive of your mums privacy, but as a general security camera covering the front door which isnt a bad idea overall for her safety but would also allow you to confirm in your own mind if he is visiting because until you know for sure perhaps you are torturing yourself needlessly.
dont take it too much to heart that you wernt able to make up with your dad he will have known deep down that you had his best interests at heart.