Inheriting a paid for house, but want to move city's and sell house. On ESA & PIP

Hello All!.. My brother has recently lost his main carer and has been left a paid for house which he will own when the deeds are changed into his name. My brother is receiving ESA and PIP and has a diagnosis of Autism. My question is will he have 6 months to buy another property, before his benefits are stopped if he sells this house?. Also he is considering renting after the house is sold rather than buying another house would this affect his benefits if he used the house sale money to pay his rent?. 
Thank you in advance.