At the end of the day, it doesn't matter who's messaging or phoning you. You control your devices, they don't (hopefully) control you.
Whatever she's doing, all he has to do is stop answering. If he's not willing to do that, you tell him you're not willing to hang out. Virtually every phone lets you set custom ringtones for specific people. He just sets hers up, and it's done. As someone mentioned, he tells her he's busy for a while, and then he ignores her. She'll get pissed at first, send a barrage of texts, but she'll get the hint eventually. Just need assertiveness and consistency. Like training puppies.