If your dad died in 2019 your mother could file a joint return for 2019. If she still has qualified child dependents for 2020 then she can file as a qualifying widow and get the same standard deduction as a a joint return, but she cannot file a joint return the year after your dad died. If she does not have a qualified child dependent for 2020 then she files Single for 2020.
What exactly do you mean by "carrying over the return from the prior year?" Tax years cannot be combined. Do not try to put 2019 information on a 2020 tax return.
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