If there is a finding of fraud in the first marriage, she will have problems. If not, and she meets the requirements for adjustment of status such as lawful entry, and not a visa waiver, then there should be no problem.
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.
As long as both marriages were in good faith it should be ok. Make sure you work with an immigration attorney because your case has a few extra complications. My firm handles marriage based immigration throughout the US.
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Legal disclaimer: The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.
It would appear that the petition was denied due to abandonment and not because of a fraud finding. Though you should have no problems in the first case I do recommend that you consult with an attorney before filing.
This is not legal advice and a client attorney relationship is not created.
I agree with my colleagues. Based on the visa she entered with, she should be fine to adjust after you get married. That is of course as long as she does not have a removal order or been issued a notice to appear before an immigration judge for being an overstay, no convictions that would prevent this from happening etc. The facts you gave are brief so based on those alone it is easy to say you should be fine. It is in your best interest to call an attorney for a consultation so that you can give all facts and get a more thorough analysis as it seems you have some concerns. Feel free to call / email my office at (904) 296-9232 or email@example.com to schedule a consultation.