The I-512 is also referred to as the "Advance Parole" document (or "card" nowadays). It "doubles up" by also serving as an employment authorization document (EAD). It's function is to let the foreign national who is pending adjustment of status (AOS) to green card to be readmitted back into the country after temporary foreign travel, while his/her AOS is being processed. One obviously travels without a green card on AP. (Had the person had a GC, he/she would not have necessitated and AP) To travel to Europe one normally needs a valid national passport, as well as a "Schenegen" visa to the countries member of the European Union. The peculiarity of a Schenegen visa is that once you obtain a visa to any EU member country from any EU member country's consulate, you are then free to travel to any and all Schengen treaty signatory EU country without necessitating a separate visa for each. Those EU countries abolished the border and custom controls among each other decades ago. The strategy for obtaining a Schengen visa is to apply for one from a "soft belly" EU member country such as Greece or Portugal (while avoiding the German or UK or French consulates), where visas are relatively easier to obtain, then with a Greek or Portuguese visa to travel to other EU countries. I hope this sheds some light.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
I do not get the question. If you are an LPR, you must have a green card or its substitute to reenter. YOur travel outside of the US is determined by your national passport and that country treaties with other countries. If you have no such passport, file for reentry permit document and yes, you will need a visa to any country you entry with it except Canada and Mexico.
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An I-512 is an advance parole card. It allows its holder to travel internationally.
(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.