Entitlement to Income Support top up to Carers allowance for Polish national

Client has been resident in England since 2005.  She has Workers registration document and has worked in the past. Between November 2008 and September 2010 she was a carer for her partner who had terminal cancer.  Her partner claimed income based ESA for both of them and she received carers allowance, her partner received DLA high rate.  Clients partner has died and cl is still receiving Carers Allowance for the run on period.  She claimed Income Support top-up but has been refused under the habitual residence test and her HB/CTB has also ceased.
Can anyone tell me if she can appeal this decision and if so on what grounds.  I am a debt adviser and this is outside of my remit so any help would be appreciated.  Cheers Sandra

Just a few questions;

When exactly did she and/ or partner come to UK?
Has she completed 12 months work for same employer under worker registration? Did the partner ? (I presume so as you say he was getting IR ESA). Between what dates were they in work?
Were they married?
Do they have dependent children and, if so, were they put into education whilst either parent was working in the UK?