Travel after H1b transfer with new passport

Recently transferred my H1b visa to Employer B and it’s already approved till 2022. My h1b from the previous employer(Employer A) has validity till 07/13/2020 and got stamped already.

Planning to travel during March 2020, have following questions related to stamping.

I understand, I can travel using my old stamping. My question here is, my passport is going to expire on April 2020, if I get a new passport before my travel, can I still travel with my old stamping from my old passport?

Pls clarify.