紧急求助; non-profit h1到non-profit h1b，有3个月gap

现在的University h1b到5月底。 新的University给申请non-profit h1b(no cap, new contract's starting date is end of August), 中间的3个月可以呆在美国么？

Will I be able to stay in the US and wait for the petition to be processed if the new school files the petition before 5月底?


谢谢！