No, you do not. If your father is still alive, he can still file a married filing jointly return in the year your mother passed away. It would get reported this way.
If it was just your Mom, then you can do a final return and include it on her return.
However, in either situation, if SSA income is all they have, they do not need to file a tax return.
In any circumstance, it would never get reported on your return.
I am very sorry for the loss of your Mom.
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