setting up iMessage on my son phone with my Apple ID
how can I monitor my son iMessage on his phone
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If you share Apple iDs you can see his iMessages, but he can also see yours. There is no way around that. Apple IDs aren't meant to be shared. You should use Family Sharing instead.
What is Family Sharing? - Apple Support
Set up Family Sharing - Apple Support
Instead of sharing an Apple ID with your child, create an Apple ID for them. Then they can use Family Sharing, Messages, the App Store, and other Apple services.
Create an Apple ID for your child - Apple Support
But I don't know of any way to monitor his messages. Unless, maybe, you setup "Messages in iCloud" for him and know his Apple ID & password. But then again, he might be able to change his password without your knowledge.
Use Messages in iCloud - Apple Support
Finally, you can use Messages in iCloud on your iPhone, iPad, iPod touch, Apple Watch, and Mac. For your privacy, Messages in iCloud is end-to-end encrypted,* which means you can't view or access Messages online via browser.