u/Inevitable_Mail_1988 — reddlx

Looking for guidance from anyone who has handled a similar case or immigration attorneys familiar with cap-counted H-1B situations.

My situation:

I have an approved H-1B I-797B valid Oct 2024 to Sep 2027.
It was approved through lottery selection with my current employer.
I never changed to H-1B status and continued working on F-1 STEM OPT.
I have been working for the same employer, but they are now not willing to file Change of Status / move me to H-1B payroll.
My STEM OPT expires June 7, 2026.
I was admitted to another university with a program start date of June 22, 2026.

My questions:

Since I already have an approved I-797B, can another employer file H-1B for me as previously counted against the cap without entering the lottery again?
Does the fact that I never activated H-1B status create issues for transfer/new filing?
Can a new employer file premium processing + Change of Status quickly before my STEM OPT expires?
If no employer files in time, is transferring my SEVIS record to the new school the safest backup option?
Is the gap between June 7 and June 22 covered by the F-1 grace period if I am starting a new program?
Has anyone successfully reused an approved but never activated I-797B with a different employer?

Documents available:

Approved H-1B I-797B
STEM OPT EAD
Passport
I-94
I-20 history
Current pay stubs
New university admission letter

Any real experiences, attorney feedback, or timeline suggestions would be greatly appreciated. I’m trying to decide whether to pursue a new H-1B filing immediately or move forward with the new program to protect status.