I am working for Employer A and will be in H1B status starting October 1st. Currently I am on OPT.
I would like to switch back to academia and have a postdoctoral offer from a university in my current city. How long after October 1st could I leave my current job and start the postdoc (i.e. switch H1B employers)? Is there anything preventing me from doing that on October 2nd? Is it possible to do this even before October 1st?
Addition I: As my H1B application has been "accepted", i.e. selected in the lottery, is it even possible for my new employer to file an H1B petition that is guaranteed to be selected? Or does it complicate things that my new employer will be a university instead of a private company?
Addition II: Is there anything preventing a cap-H1B visa to be "valid" in academia? My salary will meet the minimum requirement.