O1 is dual intent but after enter with AP, O1 is gone

My understanding:

Individuals in O-1 status with a pending LPR
application may not re-enter the U.S. in O-1 status. They must re-enter in Advance Parole as a pending LPR;
otherwise, their LPR application will be nullified. After having re-entered the U.S. via Advance Parole, the international MUST have a valid EAD in order to continue employment. The O-1 is no longer applicable.