Push new Univ. to file quick to obtain a receipt.

You are eligible to work in your new Univ. while you obtain a receipt from USCIS. You need to push the new Univ. to start your petition quick since most of the time will be spent on 2-3 wks' LCA posting. I waited more than 1 month before the school ted my peptition to USCIS. You won't be able to get H1b approval by August by regular petition, but that won't affect you.