I'm sorry for your loss. When someone dies, the person responsible for the estate is the one responsible for filing the final tax return, if one is due. That person can be the administrator or the executor of the estate, or if there isn't one, it can simply be a survivor (you).
You'd file his return the same way as if he was alive, but indicate that he is deceased and the date of death. If there is a refund due you would file a Form 1310, Statement of Person Claiming Refund Due a Deceased Taxpayer with the return.
TurboTax has a complete discussion of how to handle a deceased person’s return here.
Here is a link to information from the IRS concerning filing a final tax return for a deceased person.
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