Generally, immigration authorities will recognize a marriage as valid if it is deemed valid under the laws of the jurisdiction where the marriage takes place. Many states have laws restricting marriages between people who are closely related to each other. You and your fiance should consult with a domestic relations attorney in the state where you live about the legality for you and your fiance to become married, and if it is lawful there, then you should be able to succeed with a K1 visa application so that he may come to the United States and become married to you within the required time; then you and he may proceed with an adjustment of status application by which he would seek to become a Lawful Permanent Resident (get a "Green Card"). Of course, there are many more details about you and your fiance that can determine immigration eligibility. It would be wise for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options, and strategies to attain your goals, and who then could offer legal representation in the often complex application process. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.
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