Most Helpful Guy
This guy is out of line and I think he needs putting in his place.
What he is doing, It is a form of harassment and someone, not necessarily your sister, needs to have a quiet word in his ear explaining that if he does not stop he will be reported to the police as an internet troll who is indirectly harassing her.
Be very firm and don't take any cr*p from this guy, and be prepared to make a police complaint requesting an injunction. There is no place for this behaviour in modern society.
Explain to him that if he wants a criminal record, he is going about it the right way.
You can also report him to fb and get him closed down. But closing his fb is not enough, you have to do the first one and explain there will be consequences for him, legal ones.