H1B approved while in India for employer B and I-797B was issued

[Aj22]

Hi,I am working for employer A and I visited India in April 2021. Due to the travel ban, I could not travel back to the US. Meanwhile, my H1B got approved for employer B with I-797B was issued which does not have an I-94 attached to it. My new H1B is also valid for the same date that my current H1B validity, which is Oct 2022. Employer B said they will file an NIE request and upon approval, I can travel back to the US and i DO NOT need a new employer B visa stamped on my passport. 

Now my question is, can I do that? Because if I go with employer B upon NIE approval, I have to give a notice period to employer A, while staying in India. And upon arrival to the US, I will be on employer B payroll.

Please help. 

[LeaveMessageH1B]

IMO You will need new stamp for B

[Zodiac System]

Your visa stamp gives the name of employer A but it is not employer specific.