pensioner, Pre settled status,  and HB eligibility

hello -
Customer is Sudanese national.  Came to UK Sept 2020 on EU settlement scheme Family permit (name of person she’s joining)  - that visa was valid until March 2021, when she applied in her own right - she was awarded Pre settlement status in June 2021

She was awarded UC which ended in Jan 2024 when she became a pensioner.
She receives PIP and that is her only income now

She is temp/homeless accommodation now and has claimed HB.

I am not sure what I need to check/establish to make a decision on her HB eligibility.

She has pre settled status and inst exercising any treaty rights ( no work/self employment etc) since arriving in UK
As she came on a family member settlement visa - is is like the “old” family member rules and I need to establish what the person named on her family member visa is doing? And if they are exercising treaty rights shes ok to pay> What about if they have acquired a perm R2R? Can she piggy back that?
She hasn’t answered anything about the person named on the visa is doing

Shes applied for PCGC but no decision yet (presumably they are looking at the same sort of questions we are)
Housing are questioning how come she might not be eligible for HB if UC paid her and they have decided they have a responsibility /duty to house her… 

I feel like im trying to sing a karaoke song i’ve heard lots of times but no idea how the lyrics/melody goes…..

Any pointers gratefully received - Thanks ????