Plus she accommodated YOU by moving out 2 weeks early.

Have you taken a cold hard look at what others are charging for comparable accommodation in your area?

If they can get out and you can re rent without a loss of time or money, why wouldn't you accommodate them?

They are the best tenants I've ever had and I feel my accommodation to work with them spoke volumes of my character to be both realistic and sympathetic to working with them to get them current per their life situation. 

During that intake, they verify that the tenant is entitled to a reasonable accommodation based on them being disabled, that they meet that definition, and that a medical professional says so and that they need a companion animal based on their disability.HUD is not staffed by idiots.  

Text him back and inform him that the lease is invalid since he lied when filling in the application, regarding 3 additional people in the unit, and that he will need to find alternate accommodations.

In order to be allowed a companion animal, the tenant has to ask for a reasonable accommodation based on their disability.  

Probably no different than someone who is in a wheelchair and would require reasonable accommodations.

We are trying to be as professional and accommodating as possible without letting him run all over us.

You will need to have a Fair Housing attorney who has experience with reasonable accommodation review your policies which to me, sound reasonable.