I have a question. I am currently working with my employer A for client C. Now there is another company B that has consultants working for the same client C. They approached me with an opportunity to join B for the same client C with better pay and my client manager has no issues with me moving to company B. But then my current company A changed their names so they are going to start transfering my H1B to the new company name soon. But my question is can I have my company A and the new company B process my H1 transfer at the same time when both will have the client letter from C? ie, A is doing the company name transfer H1B and B will be doing my H1B transfer. The reason i am asking is because Company A will not do in premium and i have to pay for this, which Company B will do it for me.
Let me know if hte question is not clear.