Tenant moving and adult single son wants to take over house

[Linda Thomas]

Good evening! 

I have a long term tenant (going on 10 yrs and the rent is way below market rates). Tenant lease is up in 60 days so I sent the renewal and or option to vacate with only a $45 rent increase (I know I should have increased it by like $400 to bring it up to market rent in the area) my question is tenant wants to vacate but tenants adult child would like to stay and take over the lease. Tenant's child has been living there as well for the past 10 years. Suggestions on whether I should consider this or not? Obviously, I would make sure he meets the income requirements but the place does need some updatings and repairs so i'm not sure how to handle it? she has been a very good tenant over the past 10 years. How would I handle the move in checklist and the lease? if he was just taking over? I guess it would be considered a new tenant but she would want to transfer her deposit to him and the move in checklist when she moved in everything was in excellent condition and now it is not? not sure how to move forward. Looking for suggestions/advice as I have never had a situation like this before. Thank you everyone!