Travel to US with previous H1B visa 1 month valid and approved petition

Hi, I have my current I797 approved till May 2nd 2021 with same H1 stamping date. I got my new H1 approved from 5/03/2021 until 4/1/2024 with the same i94 dates. Can i travel to india during Feb and come back with my existing old visa ? I am not planning for stamping. Will my i94 issued based on new approved petition (Till 2024) ? Also if i receive I94 until May 2nd at POE will the extension I94 in future override the POE I94.

Your question has two parts. I will try my best to answer both.

  1. I think after going to India, you can enter with the old stamp as long as its valid and show new 797. It does not have to be on the new employer. An option for you is to utilize dropbox (interview waiver) to get a stamp with your new H1 dates if you when in India. That should set your stamp, I94 date to be good until 2024 and save you from a trip. Additionally, if you happen to travel to Canada/Mexico before May 2nd, you can skip stamping and reenter only with your new I797. At POE, the I94 system will be updated to your new 2024 date but you won’t have a physical stamp (only hand-written note).
  2. Yes, if you go to a land border/canada/Mexico your new I94 extension will be updated on system.

This may answer your question too.