H1B and other work visa notes: There is an USCIS exemption for H1 and L1 visa holders. The way this works is this: even though you apply for adjustment of status, you keep your H-1 or L-1 status, UNLESS you USE a marriage-based EAD card. What this means in real terms is that IF you do NOT use a marriage-based EAD you are still H1 or L1 and CAN travel outside the US withOUT having advance parole. Of course, you would still have to work for the H1 or L1 employer in this situation.
If you want/need to change employers, you can apply for the marriage-based EAD card when you file adjustment of status (or any time after that), HOWEVER once you USE the marriage-based EAD card, your status has effectively been changed to "pending adjustment" based on the marriage, and you WILL need advance parole to travel outside/back into the U.S. The KEY POINT is that once you USE the marriage-based EAD, you have changed your status from H-1 or L-1 at that time, and your new status is "pending adjustment based on marriage to a US citizen".
General notes about adjusting from H1B, F-1, J-1, or another type of visa: Entering the US on another type of visa, such as student (F-1) or H1B, followed quickly by marriage to a US citizen, and then followed quickly by an application for adjustment of status might be construed by the USCIS to be visa fraud. The reason for this is that you applied for the original visa, and then after entry into the US quickly applied for adjustment of status, which makes the real purpose for your original visa request suspect. Bear in mind, the onus to disprove an accusation of fraud from the USCIS is on the person petitioning for adjustment of status. For this reason, I do not recommend applying for adjustment of status very quickly after you enter the US on one of these other visa types (although filing immediately is still legal if you had no intent on marrying and adjusting status both when you applied for your original visa and when you subsequently entered the US at the Port of Entry). There is no time limitation on when you must apply for adjustment of status after marriage to a US citizen...you could literally stay in the US for years before doing so, and as long as you maintained your status on the original visa, it would still be fine. While applying for adjustment of status very quickly might lead to a fraud accusation from the USCIS , the marriage itself is not an issue--no one will try to prosecute you in any way for marrying a US citizen, even if it is not very long after you enter the US. The thing to remember is that you do not want to apply for adjustment of status until a reasonable amount of time has passed after your entry. Shusterman recommends waiting at least 60 days after entry before changing status. You may want to consult an attorney if you have further questions regarding the timing issue for adjustment of status.
General information regarding J-1 visa: Some J-type visas have a 2-year home residency requirement (2-yr HRR). Anyone who is considering marriage on a J-visa needs to confirm whether they are subject to the HRR. If the J-1 visa holder IS subject to the 2-yr HRR, he/she needs to obtain a waiver prior to marriage.
THIS URL lists the 3 bases for J-1 holders being subject to the two-year HRR requirement, and the 4 methods of getting a waiver. Actually, there is a 5th method for physicians, the "Conrad State 20" method based on job commitments in areas in which there is a shortage of health care professionals. The government-funding base for the 2-year obligation could apply to a citizen of any country. The skills-list base for the 2-year obligation only applies to citizens or residents of certain countries. There is a link to the skills list on the State Department website. The graduate medical education base for the 2-year obligation could apply to a citizen of any country.
Marriage to a U.S. citizen is not relevant to any of the 4 methods of getting a waiver, except perhaps exceptional hardship. Exceptional hardship has to be really extreme, not just a lack of employment opportunities, or problems in adjusting, for the U.S. citizen spouse, It is recommended that one hire an attorney in order to obtain a waiver.
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NOTE: The above information does not address the specific requirements for any given case and is not a substitute for the advice of an attorney.