Re-enter USA with old visa?
Answer:
File the petition and contact immigration to make sure, times are harsh dont do anything based on a guess.
As long as the visa is still valid, you should be able to re-enter on it with the new H1 approval. I am assuming the new case is already approved; if not, move the case over to Premium Processing and get it approved right away, before you leave the US. Take the ORIGINAL approval notice along with paystubs and your LCA covering your current work location and an employment letter from Employer B. Also, when you get your new I-94, make sure they give the expiration date as the expiration of the most recently approved H1 petition (if you don't, they will only authorize your stay for as long as your visa is valid, and you appear to have been authorized to stay longer as a result of the approved change of employers). If your visa is not valid, you will need to get a new one, which is much more involved than the info above.
No, because your visa stamp is specifically for one employer. If you look at the stamp, it'll spell out your original employer. You need to get a new visa stamp. Even if the port of entry officers don't catch it, if you ever plan to apply for permanent residency or another H-1B visa in the future, they're gonna wonder why the information doesn't match up.
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