M.P.
I suggest that he forgive her and then go on to act as he would if the incident hadn't happened. Except to protect himself he should expect the worse from her and be ready to be pleased if she is pleasant. Holding onto anger damages our own well being. We cannot change anyone else or their attitude. We can change ourself and our attitude. A good question to ask is "do we want to be right or do we want to be happy?"
I don't understand specifically what he's wanting advice about doing. If it's what to do for his sister who is hospitalized, what would he do if he weren't angry? He could send her a card reminding her that he loves her no matter what she's said and done. I suggest that the incidences in the past may be her mental illness speaking rather than herself and how she'd be and feel if she were mentally healthy. I suggest he show her compassion.
Holding onto our hurt and anger mostly only hurts ourselves. When experience has shown us that the other person will hurt us then we do need to protect ourselves. Learning how to do this while still showing love is tricky but well worth it. He can send her a card while not expecting love in return from her. It's a matter of focusing our ourselves and what we need; thus not allowing what someone else says or does get to us. It's a matter of building good boundaries.