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If you are a CU6, you should not become a U.S. Citizen yet. Marry your girlfriend, apply for her to get U.S. Lawful Permanent Residency and she can get it as a CU7. She would have a harder interview than normal because there is lots of fraud in those cases, but if she passes, she gets a 10 year non-conditional green card. If you instead become a U.S. Citizen and then file for her, she would only get a 2 year conditional green card then 2 years after that she has to petition to remove the conditions in order to get a 10 year green card.
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