Does she have permission already to travel outside of the country from the USCIS? If not, then she will need top file form I-131 to get approval for that, if certain criteria are met she may not HAVE to have this; read HERE for instructions for this form which is a Reentry Document and HERE to get the form itself. If she needs additional verification she can contact the USCIS customer service HERE. Having this document is the only real way to guarantee re-entry unless some other extenuating circumstance is see upon her re-entry that would have her held.
Did she apply for permission? Normally when you have a pending application you are not allowed to travel outside of the US; however you can file the form I provided for you so that you can get permission and not have to worry about not being allowed back into the US when you arrive back from an international trip. She would know if she had permission if she filed the form and received written notification of the approved application for the Re-entry Document (or it is also called Advance Parole or Travel Document). The reason it is so important for her to not travel during her probationary period of time is that it could be seen as an attempt to abandon her residency here and her application for adjustment of status. You can read more on this HERE, HERE, and HERE under Can I Travel Outside the United States?
Even though she has a Green Card, she is still a probationary or temporary status permanent resident and must file for the adjustment to get that probation removed; until she does that she can NOT travel outside the US without a Travel Document in the form of Advance Parole or a Re-entry Permit..
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