Moonlighting

I have an employee who is moonlighting and doing the exact job he does for me for customers he has sourced at night and on weekends. I have asked him not to do this and he feels he has the right to do whatever he wishes to do on his own time. I don’t mind if he does other types of work, but not specifically the work he does for me. His offer letter did not specify either way so I do not have an offer letter to refer to in speaking to him. I provided him a letter which he will now take to a lawyer. Appreciate any guidance you can provide in his rights in this regard vs the employer rights in this area.