Estate taxes for deceased with estate income less than $600

I am  the executor of my Father-in-Law's estate.  Prior to his death last January, he had about $5000 income.  After his death, his estate income was less than $600.  (He had a single NOK/beneficiary, so the assets were quickly distributed.)  I know I need to do a 1040 for his income prior to his death.  Do I need to do a separate 1041 for the less than $600 after his death, or can I just include that in his regular return, or should I just ignore it (since it is below the threshold)?