Mom selling home to my son. What should be included in the agreement?

Long story short, my Mom has been paying for 24/7 care at home (LBD but still mentally good most days, completely immobile from back surgery) and is now at the end of her savings. Her home must be sold. We had it appraised because she will eventually have to apply for Medicaid. Appraisal is $113,000 so that is what my son will purchase it for. HOWEVER, he will continue living with us here at home (he's 20) and he will RENT the house back to her for the cost of the house payment/taxes/insurance for a monthly fee of $815.00. This will allow my mom to continue living in "her" house and paying her caregivers for almost another year. I KNOW we must have a written agreement to prove to Medicaid that she isn't gifting him money every month. Would a written agreement, not a formal contract, signed by my son & my mother, witnessed by two NON-family members be good enough? What should we make sure to include in this agreement? She is willing to do this because she knows if he doesn't buy it, a stranger will and she would definitely go straight to the nursing home.