You are required to inform USCIS or EOIR of any address change.
Samuel Ouya Maina, Esq. 415.391.6612 email@example.com Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104
I agree with my colleague. You should consult an experienced immigration attorney for this matter. You may schedule a consultation with an immigration lawyer in your area, my firm is handling these matters in New York. If you would like free legal updates on these immigration issues you may sign up for our newsletter at http://www.shautsova.com .
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Wow. What a question. The facts you gave are a little confusing, since most persons who "cross the Mexico border" aren't authorized to work. I am concerned that you have been scammed by somebody.
I'm also wondering why are you worried about changing your address? Are you concerned that your case will be moved to another office outside of New York? If it is a marriage case, just because you work in a different state doesn't necessarily mean your residence is in a different state. You may commute to return to your family on the weekend or even nightly.
Whether you can work in a "different state:" well, depends what kind of a work permit you have. If you got an EAD card by filing for a marriage-based greencard, for example, it is valid throughout the United States. However, if you have an H-2 seasonal worker visa, or an H-1B visa, for example, that would be only for one employer, the employer who petitioned for you. You can't work anywhere else unless the new employer files a petition for you.
Overall, something doesn't sound right. Reach out to a good attorney to make sure you are on the right track!