No, you don't have to file a return for him for 2016. His final return would have been for 2015.
The income such as dividends that is reported in his name should be reported by his estate, if there is an estate tax return, or by the beneficiaries, which may mean it should be reported by you if you are his sole beneficiary. The investments that generated this income should all be changed over to show the new owner of the accounts.
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