H4 to H1B while H4 application is pending

[bvreddy15]

Hi,

My current contract with Employer 'A' ended 3/16/18 and in the 60 day grace period to look for a job (H1B with an approved I-140; currently looking for a job). Since running out of time on H1B status, my spouse's employer is filing H4 dependent visa for me which will not be under premium (so the process will take several months time). In the meantime, if I get land a job with some employer 'B' in next few weeks,

1. Can employer 'B' file a H1B cap exempt under premium with COS?

2. Can I start working for employer 'B' as soon as the H1B receipt is available? Or do I need to go out of USA to get the H1B stamping done?

I have an I-94 valid until 9/2019 in my most recent H1B extension, if that matters.

Thanks,

VB