Can my client claim housing benefit for accommodation which her mother owns. Mother lives elsewhere. Client claims that this is a commercial arrangement, mother needs to let out the property and has let it to client.
I am aware that she would not be eligible for HB if she and mother were cohabiting.

short answer - yes could claim but would need to show it is a commercial arrangement and not a contrived tenancy. But that only takes your client over the first hurdle. The next hurdle would be how much rent and then the son's income. How old is the son?
(oh there is never a short answer to a benefit question)
More information needed i think.

Is the client already renting the property or is there a liability to pay rent? If the tenancy agreement only comes into existence when HB appears on the horizon ("you can pay me rent if you get HB but otherwise you just live there anyway") this would raise the spectre of both a tenancy contrived to take advantage of the HB scheme and a non-commercial agreement. There are problems with consideration if the laibility to pay rent is not absolute. LAs will often ask in these circumstances if the mother would evict the daughter if she doesn't pay rent (I say often, because it's not by any means an uncommon thing, and many such tenancies do succeed). They will also wonder what the purpose of the tenancy is - I can't help feeling that an arrangement to allow Mum to pay for rent elsewhere/a mortgage etc has more of the ring of a commercial agreement than one whose main purpose is not to let daughter be homeless.

Is there a tenancy agreement? Is there a rent book? Whose repsonsibility are things like maintenance and insurance?

Lots of questions indeed. But it certainly isn't impossible.