H-1B Visa Transfer

[immihelp]

I am a H-1B visa cap exempt holder. I'm working for a non-profit organization A. I want to change the employer, and a company B already accepted to hire me. But company B is a for-profit company. My question is: can Company B ask for a transfer of my old H-1B visa, or it has to apply for a new, cap subject H-1B visa and this will be only next April? When can I start working for Company B and leave Company A?


Thank you so much!

[immihelp]

You will be subject to cap.