H1B Transfer before October

[SG809]

Hi ,

My current visa status is STEM OPT, and am employed at Company A, which filed an electronic registration for an H1B visa in this year lottery. My registration was selected in the H1B lottery with Company A, but my  employment with them is probably going to end in May/June. I have another job offer from Company B.  I have a couple of questions,

1. Is it possible for me to transfer my H1B registration from Company A to Company B and file my H1B application with Company B? If so, what would be the procedure?
2. Or, if I file a premium processing for my H1b from company A, and if it gets approved by end of May,  is it possible to transfer that H1B to Company B before October 2024, which would be the official start date for her H1B? If yes, what would be the procedure and are there any risk associated with this?

Thank you.