回複：H1B 在大學之間transfer 時間 gap 的問題

If you can show paystubs with late June employment, it should be fine if your new H1 is filed in July.  USCIS no longer enforces zero tolerance policy on H1B gap (that policy was in effect around 2006-2008)  Worse case senario is you have to reenter with h1b visa, no big deal.