Not sure if you qualify but try calling Culture Vistas
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make sure the J1 is not subject to two year residency requirement. The list of the organizations is on USCIS website.
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Most organizations will only sponsor J-1s from abroad.
(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.