Again, there's no conversion. Your new employer can apply for an H1B just as he could if you were still in a foreign country with no visa at all. At this point, if the employer is subject to the cap, I suspect you'd be subject to that. Other than a few things like cap issues, an existing H1B with one employer means NOTHING when you go to a different employer. You are immediately out of status when you quit the first job. The second job needs to apply for a new visa from you. Despite people talking about "transfer" of the visa, that does not happen.

