Bonni_mor,

Don’t move in with him.

Do get a clear understanding from him on why he wants to change his behavior.  He told you he was being selfish and lustful  Those are qualities not behaviors.  Where else is he selfish?  Is he being lustful with you?  Is he being lustful with porn?

It does not seem like he and his ex are done.  Does he still talk/text/communicate with his ex?  Do they see each other?  What will happen if she reaches out to him?  Will he respond?  Has he blocked her?

What are (good) reasons on why he should be trusted?  Does he give you those reasons?  Will he give you access to his phone on demand?

Get those answers from him before going further.

Mark