Sibling Claims Half of Mother's Social Security Paid to Me for Room and Board

I was Representative Payee for my elderly mother when she came to live with me in mine & my husband's home. When I applied to be her Rep payee, the social security agents said that I could take out 1/3 mortgage payment & 1/3 utilities from my mother's income to pay for room & board / rent. This was based on 3 adults living in the home. She lived with me for 4 yrs but eventually had to be placed in a nursing home & she passed away in the nursing home. Her will simply stated that her estate would be left to me & my brother. She had no money left in her estate at the time of her death. I had the will probated. Now my sibling is claiming that he is entitled to half her SS that I charged for 4 yrs for room & board as part of her estate. I don't see how this could be possible. He & his wife were not willing to take her into their home & he did not contribute to her care or financially. I would like to find an answer before I have to pay legal fees.

Sibling Claims Half of Mother's Social Security Paid to Me for Room and Board