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After they marry, you will need to file an adjustment package. This includes the following forms: I-130 (Petition for family member), I-485 (application for Lawful Permanent Residency), I-765 (Application for work permit), I-131 (Application for Advance Parole), G-325a (Biographic data - one for each of them), I-693 (Medical exam that a certified doctor must fill), and I-864 (Affidavit of support). They will need to file each form with supporting evidence and appropriate filing fees. You can find these forms at www.uscis.gov/forms.
The supporting evidence that they would file would be birth certificates, marriage certificate, divorce certificates if either of then have been married previously, proof of his U.S. Citizenship, proof of her legal entry into the U.S., and financial documents of his to prove his income over the last year at least.
In about 3 to 5 months after filing, she should get a work permit and Advance Parole (that will allow her to travel). About 5 to 7 months after filing they should get a marriage interview. If all goes well, a few weeks later she should get a Residency status (green card).
She should not travel until she has the Advance Parole approved and in hand which as I said can take 3 to 5 months. If she wants to try to expedite it, here is a link:
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