Let him bring himself down, without your help. More than likely, that's the direction he is headed in. Your sister's situation is probably going to get worse before it gets better. Let her know you are there for her, but don't get in between her and her boyfriend. She'll only resent you for that.

Maybe you could invite her to go shopping and have lunch with you. That way you could have time with her without boyfriend hovering around. When you're in her house, accept that you cannot "get into" it with the boyfriend without damaging your relationship with your sister. Frustrate him by refusing to argue. If he gets unpleasant, say goodbye and just leave without any commotion.

I'm sure your mom is distressed to have a daughter involved with an addict. You can't change that for your mom. Your sister is old enough to make her own decisions.

Allow things to evolve over time. This guy will probably end up back in jail.