Catherine
I can't see any way that she can claim ESA.
What is now called legacy ESA can only be claimed if the person was in receipt of the Severe Disability Premium immediately prior to making the claim, this could either be because she was already receiving a legacy benefit or because she had a Housing Benefit claim in her name and that included the Premium, neither of which appear to be the case.
So, unless she can show that she was receiving the Premium no more than 30 days ago and that she still meets the criteria to receive it then her only choice is to claim Universal Credit.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems