If a tenant dies - general advice please

Housing Benefit Overpayment

Hi. I wonder if you can help me. I act as agent for my Mum's property and her elderly tenant (of nearly 20 years) sadly passed away in February.  I'm giving his family back the deposit and checking the property etc tomorrow.  He was on housing benefit.  I'm not sure of the law on that - do they pay HB to the end of that month to allow the flat to be cleared or does the payment stop on the date of death.  It's just so I know what to advise the family as to what date housing benefit stopped. Thank you. Also should I inform Housing Benefit that he has passed or should his family do this?  His HB was apparently sent to his son's account (as the tenant didn't have a bank account) and then his son paid the rent by BACS to my Mum.    Many thanks.