K-1 visas are only available to fiances of U.S. citizens. As a green card holder, your only option is to marry her and then file Form I-130 to petition for her immigrant visa. She has to wait for the I-130 to be approved and for a visa to become available. Once those things happen, she can apply for her visa at a U.S. consulate in Sri Lanka. I would suggest retaining an attorney to help you with the process and make sure there aren't any issues in your fiance's case that would make it hard for her to immigrate. If you have had your green card long enough, you may also have the option of applying for naturalization. As a citizen, you can seek a K-1 visa for your fiance.
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