urgent help needed

I have asked this question before, but there is a recent development that I don't know what to do and need urgent help with.

I am on H1 non-cap right now. Company A has obtained H1-cap for me to start on Oct1. But I learned they do not sponsor green card. So I decided to go to Company B.

If I file a H1 transfer, do I have to have the H1 approval from company A. It seems their legal don't give it to me until I join them on Oct 1. Is there anyway I can get it without bothering them or filing without the approval. Or do I have to ask company A to withdraw their H1, and company B to file a new one.

Thank you very much for your help.