Can I file for H1B from a new company when I am on EAD

[india2us2013]

My company applied for my GC & during labor approval I got an enquiry. During the process my H1B for 6 years got expired in June 2012 & I moved to EAD sponsored from my spouse.

Now my I-140 got approved in 02/2013 so the company has applied for my H1B.

As per the lawyer, "We can file for H1B petition for you based on your approved I-140, but it will be filed for consular processing, meaning next time you travel outside of the US, you will have to get your H1B visa stamped in your passport and re-enter the US in H1B status."

So the question is once I get my H1B , can I switch job and transfer this H1B to the new company w/out getting stamped and continue on H1B at the new company and then get H1B stamped on the new company?

Your help is much appreciated