J1-h1...running out of time


New Member
My fellowship ends on june 30th 2010. My Texas license comes on june 4th, HOPEFULLY. My question is will i be ok if i submit my H1 for premium processing at that time. How soon does premium processing take place. Also can i stay in the country while my H1 visa change is in process, meaning can I stay past July 30th (after my 30 day grace period).
hope for an early reply