This should be in the lease – “No unauthorized occupants blah blah blah.” That is your written statement why he’s not allowed to live in her home.
Is he on the lease? No. Can’t live there.
Can he get on the lease? No. Can’t pass our (routine?) background check. Plus he is already on our “do not allow on property list.”
Can you put that in writing? Sure. “Your son, [name] is not allowed on property because he is not a resident with a signed lease nor is he eligible for residency [due to felony conviction if that is documented rule or due to documented complaints about him / his behavior or “has been a huge problem for years” according to the prior landlord].”
You can ask the police for a no-trespassing order and you can have him arrested if he comes on property, if you are there, or if your manager is diligent about seeking this behavior out. You are the landlord, you set the rules. You do not have to hide, you just have to tell it like it is. “NOT ALLOWED.” And then enforce it.