You have two options -
Since the 1099-DIV was issued to the deceased taxpayer's individual Social Security number include it all on their final 1040 and be done.
Get the brokerage statements for the year and separate out the dividend amounts earned and received from each of the monthly statements so that you can see the totals from before and after the date of death. The dividends paid and received all have dates on the transactions so you will be able to split the amounts in the month of death around the proper date. Enter the 1099-DIV into the personal return adjusting the amounts to reflect the math that you have done. Enter a 1099-DIV into the 1041 that is the remainder of the amounts from the original 1099-DIV.
@cher52