Precaution against H1 transfer rejection

ak1276

Registered Users (C)
I have heard that many H1 transfers now a days are getting rejected. I would like to accept an offer from company B without terminating my employment with my current company A till the H1 is successfully transferred by them. How can I do this?
For e.g. is it possible for company B to file my H1 and get H1 transferred without company A coming to know of it?
Also does a successful H1 transfer mean automatically that I have left company A or can I then after the transfer is done, file my notice and leave properly company A?
Thank you in advance for guidance.
 
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