I would have to check the guidance on cap gap to tell you definitively but I believe you can if you have not exceeded your unemployment time and you have employment. Alternatively you can wait for the H approval and obtain an H visa to return within ten days of your start date.
Lynne R. Feldman, Attorney at Law
Concentrating in Immigration and Nationality Law
2221 Camino Del Rio South, Suite 201
San Diego, CA 92108
phone: (619) 299-9600, facsimile: (619) 923-3277
Formerly Adjunct Professor -- Immigration law
University of Illinois College of Law
You should speak to an attorney before you travel as you do not want to put your status at risk.
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Please discuss with an attorney. It depends on additional items like if you are still in valid OPT status, if you have proof of an employment letter and unexpired F-1 visa. If your OPT/EAD are expired during the cap gap - no travel!
Call your company's immigration attorney and discuss your situation with him/ her.
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