Sorry about your situation. Upon your father's death, your mother will probably receive your fathers Social Security benefit amount instead of her $750. (Contact Social Security Administration about that.) Most other income, IRA, bank interest and stock dividends will probably revert to her. Also, if your father set up a pension to continue for your mother after he passed.
Most of that is conjecture, however, with the numbers you were mentioning, your mother will not have to file either. A final decedent return is not necessary and follows the filing requirements as if he was alive.
Please feel free to post any additional details or questions in the comment section.
