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A final 1040 needs to be filed for the decedent (which apparently has already been done).

 

 

The trust will need an EIN.

 

See https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-n...

 

 

As successor trustee, you should file Form 56.

 

See https://www.irs.gov/instructions/i56