No, there is no need to file. There is nothing that would be reported on current tax forms that would change the outcome of the tax forms that need to be filed after death.
The IRS is only accepting tax returns for 2018 years and prior, so there is nothing to file in anticipation of death.
Tax form 1040 is for individual income only reports the income earned in the current year. With an income of $6,000 he does not need to file.
Tax form 1041 is for estates that have income in excess of $600.
It is not uncommon for taxpayers who have not filed taxes for several years before their deaths to file a final 1040 for the year in which they died.
For more information about the taxes of deceased tax payers, follow this link: IRS on Deceased Taxpayer
