So sorry for the loss of your dad. Your mother can still file a joint return. If she files a joint return she can get the married filing jointly standard deduction which will make less of the income taxable. In My Info you can indicate that your father died and enter the date he passed away.
Did he pass away in 2021 or 2022? If it was in 2022, she can still file a joint 2022 return next year. After that unless she has a qualified child dependent she will file as Single.
Oh...and do not change the order of their names on the return.
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