There were some recent changes in the law, and it is now slightly more complicated than that. From what I understand, if the live-in partner contributed in any way at all towards the up-keep of the property they can claim a compensation. So if he paid for the double-glazing then yes, he can claim some money back of what he contributed. As to the rest of the house your mum might have to prove that she was solely responsible for mortgage and other payments.
With the regards to the notice, if the solicitor admitted that they were aware that the house was empty and you would not receive it then you have all the rights to contest it.