I assume this is a continuation of another thread?
You do not have to prove to the IRS that he moved out in June, unless you are audited. Then you'll need something to substantiate that he moved.
I would keep a daily journal. Maybe a neighbors written statement. Did you change the phone, gas & electric, water bills? If you rent, did you get his name off the lease when he finally moved away - ask the landlord for a written statement. Did he quit his job and move out of the county or state at the same time? If so, and if you know where he worked in July, see if that employer can provide you with something. Heck maybe even a text message . . .