Its virtually impossible to get a waiver from Fullbright. But if you want to try hire competent immigration counsel and they can apply with the US State Department.
I agree with my colleague. You should consult an experienced immigration attorney for this matter.
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You probably changed your status to H-1B rather than getting an H-1B visa.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
You are subject to the two-year foreign residence requirement on INA § 212(e) based on U.S. government funding.
Being subject to the requirement creates 3 legal disabilities that do not go away until you obtain a waiver or fulfill the requirement by residing and being physically present in your country of nationality or last permanent residence (at the time of J-1 admission). These disabilities are: (1) you cannot apply for H or L visa stamps; (2) you cannot apply for a green card; and (3) you cannot apply for an immigrant visa.
Your H-1B status was improvidently granted. You likely changed your status from F-1 to H-1B. You are in H-1B status, but it is revocable by the USCIS.
There are four kinds of J-1 waivers. These are: (1) no objection waiver; (2) hardship waiver; (3) persecution waiver; and (4) interested government agency waivers, of which there are many varieties.
Options (1) and (4) will likely not overcome the special problems associated with the U.S. government funding. The Department of State Waiver Review Division (WRD) stringently enforces the two-year foreign residence requirement when U.S. government funding is involved.
Option (2) may work if you have a qualifying relative or relatives that would face exceptional hardship in all travel alternatives. A qualifying relative is a U.S. citizen or lawful permanent resident spouse and/or child or children. The hardship must be truly exceptional to overcome the special problems associated with U.S. government funding.
Option (3) may work if you can prove that you would be persecuted upon return to your home country on the basis of race, religion, and/or political opinion.
For these reasons, I recommend that you consult with a lawyer that has experience with J-1 waivers, in particular J-1 waivers where U.S. government funding is involved. I recommend you ask such a lawyer whether they have had success with waivers that involved U.S. government funding.
Hake & Schmitt
Attorneys at Law
P.O. Box 540 (419 Main St.), New Windsor, Maryland 21776