My boyfriend's ex keeps trying to contact him?

[Tay]

She broke up with him a bunch of times, and they had a very rocky relationship. They ended it for good about 6 months ago. She was saying all this mean stuff about him on twitter and facebook like "he's a fucking loser, so glad to be rid of that pathetic jackass" and stuff like that. She even sent me a facebook message saying "I hope you have fun with my secondhand toy "

I wish this psycho would just leave us alone, but she's been texting him lately asking if he wants to hang out. He says that he declines, but I don't know if he's even telling the truth or not....

How do I deal with this??