I am working in NYC, and my first term H-1B will expire in Sept. Since I plan to move to Texas in one or two month depend on when I can find a job there. If I extend my H-1B in NY, and then I find a job in Texas (non-profit employer) before my extension get approved, can I directly start to work after my new employer file a H-1B application? Please give me suggestion. Thanks a lot.