Good tenant has new partner moving in w/ past eviction + bad cred

[Eli Altman]

I have a tenant in good standing who has a good job, pays on time, is responsive and responsible. He broke up with his partner (happens) and has a new partner who is moving in. He was very upfront about this and introduced her to me to do an application/screening. 

Credit came back with 2 delinquent accounts. I don't rule out solely on bad credit but I tend to focus on delinquent payments. And, much bigger issue, she has a past eviction in the same town as my property she's moving into (Northern California). So, bad tenant I would have never rented to if she was applying on her own.

Not sure the best way to proceed. What do I communicate to the tenant? Is it worth losing a good tenant mid-lease? I don't even know what I'm allowed to do here. I do know he can cover the rent on his own. Is it better to have her on the lease or not? 

What's the best move?

Thanks.