I was an MBA student and graduated in Spring 2019. I am currently employed by California State University, and they filed for my H1-B this year and USCIS received it on March 27. Since my OPT EAD expires on July 10, 2019, and the processing time currently is between 2.5 to 4 months, I was wondering if I am eligible for the Cap-Gap I-20 since my employer is a non-profit organization and the H1-B is cap-exempt. I would really appreciate your insights on this situation.
Unfortunately, it does not apply to cap exempt employers like you said. See below the guidance on USCIS website. Check USCIS website