You may use your employment authorization document to work for another employer. However, I recommend that my H-1B clients maintain their H-1B status until their permanent resident application is approved in case something goes wrong with their permanent resident application. This way, the H-1B status serves as a back-up to keep you in status if your application for permanent residency through your wife fails.
Elizabeth Rompf Bruen
Attorney at Law
Scott D. Pollock & Associates, P.C.
105 W. Madison Street, Suite 2200
Chicago, IL 60602
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