Tenant wants to add boyfriend - as sublet

What should I do.

Tenant so far has been very good.

She just recently asked me about adding her boyfriend. She is a single mom recently divorced past 2 years with 3 kids and has a good job and is  a quality tenant so far. 

She asked if she could move her boyfriend in. I had him fill out an application and do a credit report. He has awful credit and I can't verify his recent rental history seems sketchy self employed past 8 years not verifiable. Past child support arrears on credit bankruptcy under 550 score. 

I would not rent to him. 

What do I do. 

She wants to remain primary responsible for rent. 

Do I ad an addendum that he is allowed to reside there not liable for rent. 

I would not rent to him.