Lodgers, Council Tax and Benefits

I'm moving in with a friend who is unemployed and in receipt of JSA and Housing Benefit/Council Tax Benefit. She is trying to sort out the council tax situation. As I understand it:

- Anything I pay her over £20/week rent affects her benefits
- She loses her single person CT discount when I move in
- As she is the only person named on the tenancy agreement, it isn't possible for us to have joint names on the CT account. (this is what the council told her)

So, this being the case, how do we best arrange the Council Tax payments? She currently has to make a contribution on top of her CT benefit, because of her spare bedroom (which I am moving into), but my understanding is that if I give her money towards the CT, it comes straight out of her JSA, so doesn't actually help her pay the bills at all. To me, the simplest approach would be for me to simply pay whatever is left after her CTB pays her share directly to the council, but I don't know if this still counts as 'giving her money' since she is legally the one responsible for CT.

Any thoughts or advice on this is appreciated.