I am doing postdoc with H1b via at university of virginia (UVA), and I'm going to transfer my H1b to Harvard. Harvard is going to file my H1b application to ICS within this month of May(job starting day is some day within this month of May). The problem is that UVA is going to terminate my employment at the end of May. Will the job termination cause me any problem? Please advise if it will affect my immigration status and my application for green card later if there is a gap (unemployment)before the employment by Harvard.