MRVP voucher applicant does not want to add live in boyfriend to lease

[Sylvie Manning]

Hello, This is my first time renting my condo and I have a family (woman and her 2 children and her boyfriend) wanting to move into my condo. The mom has the MRVP voucher for her and her kids, but does not want to add her partner (who makes the majority of their income) to the lease. 
I ran a credit/background check (which are clean, she has a 630 credit score and he has a 560), they have stunning references from work and employers. 

I believe she does not want to add him to the lease because this will impact her ability to receive the voucher. I do not feel comfortable moving forward with the applicant without the partner on the lease as well. 

Please advise, I want to make sure I'm not discriminating and doing this above board.