As a UK citizen there won’t be as many hurdles to jump, but on returning she must immediately register with a GP, get assessed and ask for a letter of support once they have seen her. Because she has family in the area, who have presumably lived there more than 5 years, she will be considered to have a local connection.
Make sure she has all paperwork from previous doctors to support the claim of long covid. And I mean ALL. You can’t be too over prepared on this front.
Keep copies of end of tenancy agreements to prove she has left the EU country where she has been- get a letter from landlord to confirm if possible.
Keep documentation regarding travel i.e tickets and visas
Open a bank account in the UK, get copies of opening statement and also print out 6 months history from her previous banks.
Get a copy of her birth certificate. Make sure she has her passport.
All this can be done using your address and can be changed later.
Lack of preparedness with regards to paperwork is the SINGLE biggest reason for delay when it comes to engaging with your local councils housing department.
Present as homeless to your local council. Take a letter signed by you or your mum to say you refuse to house her.
She WILL be placed in Temporary Accommodation. She might not be in your district - ours houses people in adjacent council areas or wherever there is space. Given how much support she has for her medical condition, she may be considered priority need with regards to how soon she will be found permanent housing.
All this can be happening while she is going through Habitual Residency
She can start an application for UC and housing benefit. ( it will be HB not the Housing element of UC as she will be in TA). This will run alongside her Habitual Residency period and payments will be backdated. The application for UC will trigger the Habitual Residency test interview.
Hope this is helpful. I work for a local authority and alongside its housing department.