You should apply for your green card when you are eligible (one year after your asylum grant). Then you can file for a green card for her, but it will likely take a couple of years.
www.gassonlaw.com - Disclaimer: This a general answer to your legal question. Unless you have a signed engagement letter with me, you should not consider this information to be legal advice.
You're right that she won't qualify for the I-730 since you weren't married at the time you got asylum. You can marry her now if you'd like, but you'll have to wait until you get your green card before you can petition for her. After you petition for her, it will take a few years before a visa is available for her to come to the U.S.
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I agree with my colleagues. However, I would strongly suggest that you use an immigration lawyer. There is much more to our profession than filling out forms. There is a lot of analysis that occurs behind the scenes. Get a lawyer and do it right the first time. Repeating anything in the world of immigration is on a time scale of months or years. As a result, it can easily cost you more time and money to obtain an immigration benefit on your own than if you use an attorney. Plus, keep in mind that there are significant “opportunity costs” as well. (A good example is where someone has to re-submit a work permit application and wait a few additional months before working).
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Dean P. Murray
The Murray Law Firm
560 Sylvan Avenue
Englewood Cliffs, NJ 07632
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There is no visa you can file for your fiance until you become a permanent resident. There is about a two year wait for the visa, which you can file at that time.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.