I have the impression that one do can work with current H1b visa after parole back with AP. But below is what I got from my school lawyer---it looks that you have to work with EAD or apply for new H1b.
Anybody has any suggestions and opinion? ANy inputs are appreciated!!
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if you choose to travel and return to the US under advance parole, you
will not be in H-1 status, and, therefore, can't use the H-1 as a basis for
employment authorization. You will need a valid EAD in order to be eligible
for employment after being admitted in advance parole, and your I-9 must be
so amended.
CIS has, in precedent, changed the status of a parolee back to H-1, upon
consideration of a petition filed by the employer. If this is what you
choose to do, you will be without work authorization for the period of time
between your entry and the approval of a petition, if granted. We couldn't
give any kind of priority to a case like this, so you would likely be unable
to work and be paid for a month or perhaps longer.
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