We're excited to announce that we've fully migrated the Xbox Forums to their new home, here on the Microsoft Community forums!
As of today, going to forums.xbox.com will redirect you here to the Xbox area of the Community forums. We've moved all of your existing threads over so you can continue and start conversations with the new forums experience.
We sincerely appreciate the feedback you have provided over this transition and can't wait for you to check out the new Xbox Forums!
As the others have said, sadly, no. There's no way to retrieve messages once they've been deleted. However, assuming your son's account is a child account attached to a parental account under your control, you can make it so he can not message other people
on Xbox live at all, among other settings to restrict what your child can do on Xbox Live.
Here is the guide on how to utilize Xbox Live's parental controls to the fullest: