Filing Form 709 for Deceased

My father passed away last year after giving a gift greater than $18,000 to a single recipient. He did not file Form 709.

 

Instructions for Form 709 state "If a donor dies before filing a return, the donor's executor must file the return".

 

However, we never had an executor formally recognized in court, as my fathers assets were placed in a living trust to avoid probate.

 

Thus, I was wondering who can file Form 709 on behalf of my father if there is no court appointed executor.