COS to H1B while COS to H4 is pending

[aa11]

Hello, I am in a tricky situation, please help.

I was working with Employer A on H1B status. Employer A terminated my job may 2021. I searched for a new job couldn't find in the 60 day grace period. The 60 days from termination date are passed now.
But before 60 days grace period was over, I filed for a COS to H-4 dependent based on my spouse's current H1B employment. I received a notice from USCIS that my application is pending. The received date is 1 week before the 60 day grace period was over.

Some background: I have been on H1B for last 5 years, 1 year before that on L1-B. My I-140 is approved from a previous employer X.

Questions:

1. Now a potential employer B is asking me my current immigration status which they need to record. What should I say - H1B, H-4 or something else, since H1B employment was terminated and H-4 petition is pending.

2. If employer B wants to file a cap exempt H1B for me, can the COS to H1B happen while COS to H4 is in process Or will I need to go out of the US to get either H4 or H1B stamped?

3. I am an Indian citizen and If I need to get H4/H1B stamped, I heard consulates in India are closed. Which country can I go to to get the visa stamped?

[Zodiac System]

Your current status is - Pending H4.  Employer B should be able to file cap exempt H1b COS, while H4 is being processed simultaneously.

[aa11]

On 7/26/2021 at 6:35 AM, Zodiac System said:

Your current status is - Pending H4.  Employer B should be able to file cap exempt H1b COS, while H4 is being processed simultaneously.

Can the COS to H1B happen while COS to H4 is not yet approved or will I need to travel out of the country?

[Zodiac System]

COS to H1b can be processed simultaneously with H4 processing.  You can be only one status at a time.  Once approved, you can decide if you want to be on H1b or H4.