What to do with my boyfriend's ex?

So my boyfriend and I met at school. He had to move back home, all the way on the other side of the country, because his dad had a heart attack. So its a long distance relationship.

His ex-girlfriend lives six hours away from him. He does not like her but he does pity her and he always feels guilty when it comes to our situation because in October she found my facebook and she basically just messaged me and told me to take care of him. I called him and we had this long discussion about it all. He told me he broke up with her right as soon as he started school, the relationship was not a real, healthy relationship and that he was only with her because he thought he could help her and that was the first time he said that he loves me. The next day she sent me really mean messages on Facebook. She also tried telling me he wanted to be with her, that she text him telling her that he wanted her back. And my boyfriend like basically sent me screenshots of the texts she sent him.

This girl is way older than me, she has called me horrible names, has tried to convince me my boyfriend is trash when he has been nothing but honest with me. He's always there for me and he always makes sure I'm happy. The last contact I had with her was last month and that was accidental but she messaged him a few days ago on facebook and he was so tempted to message her back but i asked him not to because i really think in order for her to completely get over him and not try to bring up old feeling is to just kind of not communicate. Is that wrong? Was that wrong of me to ask him to not message her back?

Because i don't know what to do about her because I've called her out on her behavior and she says she is doing nothing wrong.
What to do with my boyfriend's ex?
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