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form 706 is not required unless her estate was in excess of $12 million. a  Federal 1041 is required.

the federal ID# is never closed. you just file the 1041 as final. New Jersey does have its version of the 1041

instructions for NJ

https://www.nj.gov/treasury/taxation/pdf/current/1041i.pdf 

 

 

estates and trusts can be tricky. federal - if there was income was it distributed in a timely manner so it's the beneficiary that pays the tax.