Alistair, it looks to me like your neighbour has already discharged her [or rather her mother's] obligations to OVO. A letter to OVO re-stating your neighbour's position is the only further action I'd advise her to take.
If OVO insists on transacting business henceforth directly with her mother, your neighbour might like to tell OVO that they are perfectly free to do so.
We had a similar situation with a supplier in the case of my father, who has severe dementia and whom we have POA for. The company alleged there was a sum of several hundred pounds outstanding on his account. We told them there wasn't [and indeed there wasn't].
The company insisted on dealing with my father directly. We said they were free to do so, but that whether they dealt with us or our father they would never get a penny because of our certainty, on the one hand, that the bill was wrong and because of our father's incapacity on the other. Within three days we got a letter saying the matter was closed.
Another piece of advice I'd give your neighbour. Don't ring OVO – ever; write to them instead. There are several advantages to this, which I will leave it to others to identify. I have not rung a utilities company for any reason connected with billing on my own or another's behalf for around four years. My life is appreciably the better for it.