H1 (Employer A) to H4 (Visa Stamp) to H1 (Employer B) -> Can I enter country with H1 (Employer A)?

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Hello,
I need some help regarding entry eligibility with previous H1B stamp.

Here is my scenarios

  1. I have a valid H1 visa stamp with Employer A, it is valid till Aug 2022.
  2. I switched to H4 in 2020 (COS), also entered country with H4 visa stamp in 2021 (Apr).
  3. I switched to H1 in 2021 (Aug) and have approved I-797A with Employer B.

Can I use H1 Visa stamp with Employer A for travel purposes? i.e. use H1 (Visa stamp Employer A) + i797 (Employer B) at port of entry and enter on H1B?

Yes, absolutely! Visa is just a travel document and not tied to an employer even if it may have employer name & petition # on it. So as far as the visa is valid you can use it for travel along with the current I-797, no matter what employer.