Yes, I think you need to tell the other parent about the shoplifting. I would keep it simple and just deliver the facts as you know them, and let him know that you would want to know if you were in his shoes and that's why you are letting him know. And you're telling the dad so he can help his child and talk to him about it.
You can tell your kids that you are telling his dad and you can talk to them about WHY you are talking to his dad. It takes a village