F1- H1/B where company is not e verified

[Akshaya Sriram]

I work for a company that is not E-verified. Currently I am on my 12 month OPT and it expires June 9,2020. Also, my current company is willing to sponsor my H1-B, filing April 2020. I have the following questions:

 

1. Given that I need to start OPT extension procedures 3 months in advance, and I have an offer letter from an E-verified company that starts on June 10, 2020 (One day post current EAD Expiry Date), can I process my OPT Extension with this company? (while currently working for my current company).

2. My current company (Non - E verified) will be filing my H1-B for April 2020 slot. Given that my H1-B gets approved, can I inform to USCIS that I have my H1-B approved? Does my status change automatically? In this case then

-What happens to my OPT extension? Can I continue working for my current company in which I have my H1-B Approved?

- What happens till Oct 2020 till H1-B stamping happens, given that this company is not e-verfied?

Thanks a lot for your time on my post! Really Appreciate it.