Someone did mention "executor."  Trusts don't have executors.  Estates do.  At least in backwards states like New York that have not adopted the Uniform Probate Code terminology of "personal representative."

Georgia is decided unfriendly when it comes to instructions for its Form 501.  However, they eventually state that "every resident and nonresident fiduciary haivng income from sources within Georgia or managing funds or property for the benefit of a resident of this state is required to file a Georgia income tax return on Form 501."  

He's a beneficiary, right?  I don't think his status as executor creates the filing requirement, but if he's a fiduciary for himself, managing property for his own benefit, I wouldn't want to argue that he doesn't have to file