I'm not going to tell my father in law where his former tenant lives/works
Why don't you want to tell him?
I'm not on speaking terms with his son
Even if you were on speaking terms with him or his son, you should not give up the personal information like that. People deserve to have privacy, if they wanted to let them know they would.
I know that.
Then there isn't a problem, then. Keeping former tenants privacy private is the right thing to do.