If the SSA 1099 has your name and social security number, then it goes on your return. See Where do I enter an SSA-1099, SSA-1099-SM, or SSA-1099-R-OP1?
All income earned by your father until his departure, is filed on his final 1040 return. The IRS has a quick How Do I File a Deceased Person interactive assistant. It is very detailed and may give you additional information, including estate help.
For additional assistance, please refer to Publication 559, Survivors, Executors, and Administrators
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