Your daughter has a good handle on this situation. When she gets tired of it, she'll either delete the messages or block them.
No, I don't think your h would be more aggressive with initiating a real phone conversation. If he is reaching out, it could take months before he actually works up the nerve and phone her and actually act like a mature adult. If he's reaching out, he's stepping lightly to see how things are and if she's willing to allow him into her life after all of this time.
Again, I think your daughter has this. I wouldn't worry too much about it unless she comes and talks to you about it. I would then listen and offer advice if she were to ask for it.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.