The trust document did not require a separate irrevocable trust to be created at the death of the first grantor.  The trust document says "upon the death of either of us, the trustee  shall continue to administer the Trust as provided in the preceding articles"...., and the Trustee shall receive any amounts devised under the terms of the deceased last will, which defines the surviving spouse receive everything, and the Trustee shall continue to hold the Trust Estate for the benefit of the Surviving Settlor, to the exclusion of all other persons."  

So I guess this Joint Grantor Trust, upon the first grantor die, is treated as both the deceased grantor's estate and the surviving settlor's revocable trust?  

Bob you are right I am not experienced in reading the trust document and did not realize I didn't have one yet.  I just received it today, as a result of receiving your critiques and realized the "trust certificate" and the "Will" combined together could not serve as the trust document as the client claimed.  Thank you.  

The Joint Grantor Trust was using the deceased SSN as the TIN, and did not file any Form 1041 from 2019 to 2020.  I think an EIN needs to be applied for this trust to file its first tax return. 

In this case, how should I report the capital gain with 50% attributable to the surviving wife using her own original cost basis and the other 50% attributable to the deceased husband with a stepping up cost basis?  

P.S., is it correct that after the first Grantor dies, the Joint Grantor Trust survives as a revocable trust, but the structure of the trust becomes Estate Trust within the Joint Grantor Trust in substance?  I wonder if it is correct to apply for an Estate Trust EIN for the decedent to report the Cost basis step-up, and then report 100% distribution to the joint grantor trust now only have one trustee, and report the original cost basis release on the surviving wife's Form 1040.  This way we just need to file one Form 1041 and one Form 1040, no longer need Section 645 to make an election.