Pending COS-F2 to H1B transfer

[terrible_coder]

I hold an H1B visa as a foreign national. Following my departure from my previous employer on May 01, I have submitted an application for a Change of Status (COS) to F2, as my spouse is on F1-OPT. Currently, my COS-F2 application is awaiting a decision from USCIS. I have received a job offer from a potential employer who is willing to initiate the H1B petition process(premium processing) to facilitate my transfer from my previous employer.
 

1. I'm interested in understanding whether I should provide my prospective employer with information regarding my COS-F2 application?
    
2. Additionally, I would like to know if my new employer needs to include details about my COS-F2 application when filing the H1B I-129 petition?
    
3. Would USCIS automatically give precedence to the H1B petition over COS-F2? or do I need to leave the USA and get a new visa stamped and return back to the USA?

[Attorney_23]

Generally speaking, if a person's 60-day grace period has passed, they may remain in the U.S. in a period of authorized stay based on a timely filed application to change status that remains pending. While it is pending, if an employer wishes to file an H1B change of status for the individual, it typically would be recommended to include information regarding the pending F-2 application.