Yes, you can. The H-4 extension isn't really based on company A - it's based upon your spouse being married to someone who is maintaining valid H-1B status.
As long as you are on a valid H-1B, there is no threat to the H-4 (may need to be proven with filing receipt for company B case, pay statements, etc.) You DON'T need to file another H-4 along with your change-of-employer petition for company B.
The thing to watch out for is that the H-4 and your new company B H-1B will probably...
I agree with my colleague - you need to speak directly with an immigration attorney about this.
You say he was deported twice - if this is actually the case, he may be subject to a permanent bar to return - no waiver will help with this.
Speak with an attorney.
I agree with my colleague generally, just want to note a couple of items: to be eligible for a new full period in H-1B/L-1 status through a "re-set," you need to have spent a full 365 days abroad - any time spent here, even as a visitor, would be subtracted from the year you need to spend. So if you go to the consulate to get a new visa based upon an Approved USCIS H-1B petition, and they determine that - for example - you spent a week here as a visitor in June 2014, they will deny the visa...
It generally takes 10 days to just over two weeks to get the Receipt Notice back - so not overdue yet.
Can your employer/their lawyer track to make sure the package got there/? Have filing fee checks been cashed, and if so can the cancelled checks be viewed online? Often the receipt number will be visible on the endorsement.
Discuss with an attorney directly.
I agree with my colleague - if you are here, generally speaking you can apply to adjust status while here. You need to speak with a lawyer to see if this is a real possibility (there are a few reasons this may not work).
If you file for adjustment of status here, leaving before approval without permission - called advance parole - causes abandonment of the pending application (so, do NOT leave for the UK before you get this). It does take about 90 days for the parole to come through....
A Permanent Resident would qualify for the FMLA as long as the employer is required to provide benefits under the act (some smaller employers may not be required to provide FMLA benefits for any employees).
Generally speaking, distinguishing between Permanent Resident employees and US citizen employees in terms of qualification for benefits would be considered discrimination on the part of the employer.
The SSN doesn't have much to do with FMLA eligibility (though a permanent resident...
The fact that you are already in removal proceedings makes your case very complex - and urgent. It's possible you may have been better off filing a new marriage case before the Notice to Appear was issued (they may have decided not to issue one - but this isn't certain).
However, now that you are in proceedings, the interview will be a far more complex one with a much higher degree of scrutiny. And, you need a lawyer to deal with the removal case as well as prepare you for what would have...