No, your parent's income is never reported on your tax return.
If the final return is filed on his behalf, the form would be included on his tax return.
This is a follow-up question to the above, but with more specifics...
When my wife's mother passed away in Dec 2018, a check for final SSI was sent to my wife (serving as estate administrator) and paid out in Jan. 2019. We later received an SSA-1099 for TY19. On the SSA-1099, Box 1 lists my wife's name even though guidance on the back of the form says "'Name' - shows the name of the person for whom we paid benefits." Furthermore, Box 7 lists "[Wife's Name] On Acct of [Mother's Name] Dec'd".
The money received was part of her deceased mother's estate. As such, I don't believe it's part of our (MFJ) income. Is that an accurate assessment?
This is a tricky question but this is a taxable document that needs to be reported in a return. Since this final owed Social Security benefit was late received, and therefore could not be filed with the Final Form 1040 for your late mother. Instead the benefit was written out in your name, with the annotation Wife's Name] On Acct of [Mother's Name] Dec'd.
If you received the benefit check or benefit deposit, then this is "Income in Respect to a Decedent" (IRD) and is reported as if it were your income. So you would report this as a social security benefit in your own return.
The one other question is whether or not your mother's Estate was large enough to require Filing of a Form 706 Estate Return and pay Estate Taxes. If you did this, there is an available deduction for the Estate Tax paid (not income tax paid).