Your deceased's sisters actions could be regarded as fraudulent as she did not carry out the purpose of the agreement which was for your mother to move into the extension.
Your mother does not a beneficial interest in the property where her funds were invested. She has made a contribution in money or moneys worth" to the property and improved it's value.
As her Attorneys you can claim against the property which would be vested in the estate of your sister. So your claim would be against the executor of your sister's estate in respect of your sisters interest in the property.
then it may be possible to negotiate a voluntary charge on the property in respect of any future fees .
Sorry there was a problem my response above which has sections missing from what was typed by me. Your mother DOES have a beneficial interest in the property where the money was invested
The final paragraph only partially came through. This related to a claim by the local authority for any care fees once the cash is depleted based on your mothers interest in the house.
This can be dealt with by way of selling the house or the local authority may agree a voluntary charge on your mother's interest in the house if it is still being used as a family home