Pension Credit or Universal Credit?

Hi
Hope someone can offer some guidance.

I have a mixed age couple overseas British Territory with British passports ( have come to England from Turks and Caicos on 11th April 2019) with no income.

Mr aged 71 with health issues, Mrs is his carer aged 57.

Are living with family in England hoping to get social housing, have GP and social worker.

I am thinking of arguing that they have habitual residence after 1 month (or earlier) so that I can make backdated claim for PC ( back to pre 15th May 19)

Or do I advise them to claim UC with carer element (Mrs)  and LCWRA element (Mr)(despite his age), Mr cant claim AA yet until he has met past presence rule.

If PC is knocked back pending challenge could they then claim UC and if PC is subsequently allowed can everything revert to PC or are they stuck on UC?

Advice greatly appreciated :)

I can’t comment on the chances of success you’d have with the habitual residence after one month, but I do know that if they decide to claim UC while challenging a decision refusing PC, they will not be able to go back to PC, as the PC award will terminate the moment entitlement to UC begins.