Benefits are total muppets when it comes to this, though I do think that it's right. Why should they pay her money when they still think that he is living with her.
He does need to get his address changed.
If she contacted the people that she rents off, they should be able to help as she obviously needs to now have the tenancy in her sole name (sorry I'm assuming that she rents). When she's got the tenancy agreement, she can pass it onto the benefits office. Thing is though that housing benefit don't usually backdate, and I don't know if the Jobcentre are the same.
IMO, she needs to arrange to see someone at the Jobcentre, explain her situation so that it is logged on their system (they have special people for lone parent applications) and then when HB/the council come back querying it later, they can refer back to the Jobcentre and fingers crossed that it'll be sorted.
Please can you remind your friend from me (as your mentioning her benefits I'm assuming that she's unemployed) - that after she's been off work for 26 weeks/6 months, being a lone parent, you get a £250 back to work job grant and also £40 a week "in work credit" for the first year. I hate to be teaching granny to suck eggs, but a lot of people are unaware of these and its really helped me this last year. I'll be skint in December when the weekly bonus stops, but it's really made the transition back into work much easier :)
Best of luck
Sarah x