JSA turned down as unable to provide sufficient proof for Visa restrictions.

I would really appreciate some help as I am a bit lost as to what to tackle first.  This lady had exceptional leave to remain in this country until 2nd October 2005.  She was in receipt of income support and then ESA.  On 24th August 2005 she instructed a local solicitor to make an application for Indefinate Leave to Remain. That solicitor did not send this application to the home office until 12th October 2005.  She was unaware of this. She heard nothing from her solicitor or the home office for some time. In 2007 she recieved a letter from another firm of solicitors advising her that they are now acting on her behalf.  The solicitor that she had originally instructed had left the first firm and moved to the new firm and had taken her file with him without consent.  The new firm of solicitors then took no action on her case so she lobbied her local MP.  She was not very sympathetic and was unable to change things for her she also did not pay any attention to the original receipt. On 21st January 2011 her claim for ESA was stopped and she was advised to make a claim for JSA after a medical assessment decided that she did not have any limited capability for work.  She then made a claim for JSA. DWP request proof that she applied for Indefinate Leave to remain before the 2nd October 2005.  She could not provide a letter as the solicitor did not provide this.  He did however provide her with a reciept dated 24th August 2005 written on it “Recieved with thanks: Application for ILR and £100”.  I have a few questions: Firstly, Can I appeal the original DWP decision for JSA dated 15 th Feb 2011 under the provisions of a late request for “any grounds revision” stating the above. She has not requested a statement of reasons.  However, I am confused that they have not questioned her eligabilty to the benefits that she had received since 2nd October 2005 is there anything there that I can use?
Secondly, would the reciept from the solicitor act as proof that the application for ILR was made well in advance of the 2nd October? Thirdly, is there anything that the new solicitor should be doing given that she has not heard anything from the home office for a number of years.  Many thanks for any advice.

I agree with Tony, step one has to be establishing her immigration status… then benefits advice.