I have had this situation. We continued to fund the Bypass Trust even though the spouse had passed away. The assets transferred to the Bypass Trust are valued as of the date of death of the first to die.
The Survivor's share would be included on his/her Form 706. The existence of the Bypass Trust would be indicated in answering the Questions on page 2 or 3.
I once asked an IRS Estate Tax Attorney how this would be handled if it was a stale trust - one that hadn't been funded for a number of years after the first death. He said that the IRS would allow a deduction as a liability for the unfunded trust. That seems to raise basis issues for me, but that was the story. Mary Kay Foss