Hi, what happens in the following scenario:

1) I am a H-1B visa applicant for the first time. Company A sponsors my H-1B visa.
2) The petition gets picked up in the lottery. It gets approved and I get the visa stamped on my passport.
3) Lets say, A cannot find a client for me or for some reason, I do not like the client/work. I don't join A and my job offer expires. I don't even travel to US on H-1B.
4) Now, after several months, I find another company B which I like and want to join. B is willing to do H1 transfer.

Can B file a cap-exempt petition? Is there a time limit within which B has to file the H1 transfer?