If you and your US citizens significant other get married and file for an adjustment of status, you will not be violating the law by staying in the United States because you will be "in process" to adjust. There is no "best time" to apply for adjustment of status -- the best time is the time you get married and are capable of applying via I-485 for adjustment of status. As part of that application you may also submit an I-765 to obtain another EAD extension. I think consulting a competent immigration to help you through the process may be very valuable to you.
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Since you entered US legally through inspection, and since your future spouse is a US citizen, and provided you are otherwise eligible for adjustment of status, you may remain in the US while going through the adjustment of status process. Nevertheless, I would highly recommend that you hire an experienced immigration lawyer to assist you with the process.
Contact immigration attorney Gintare Grigaite, Esq. at 201-471-7989, located in New York and New Jersey. Contact immigration attorney Gintare Grigaite, Esq. for a free consultation about new Immigration Reform policies. Answers on AVVO do not constitute legal advice and do not form attorney-client relationship. Always consult an attorney for a legal advice.
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I agree with the posted answers. You will not have to depart the US on June 12, 2013 assuming you have a correctly filed and pending green card application prior to that. I highly reocommend you do not file the green card application by yourself.
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