Please consult with a qualified immigration attorney before proceeding. If your wife was inspected and admitted, has not left, is still here, and has no other bars to admissibility, she can simply adjust once husband becomes a U.S. citizen - that would be worth the wait for him to naturalize, assuming he is able to do so. If she has to consuar process, she may have already triggered a ban on lawful reentry depending on how long she has remained here out of status. She wuodl need a waiver, and can apply for one, but would have to do a traditional waiver if husband is only an LPR. If husband were a USC, she could do a provisional waiver, but then she wouldn't need one, because she would be eligible to adjust. An immigration attorney can help you flesh out all the specific facts and circumstances of your case and can best advise you on how to proceed accordingly. You can search for an immigration attorney at www.ailalawyer.org. Best of luck to you.
The best thing you can do is speak with a reputable immigration attorney. From what you describe, there are many additional questions that would need to be asked of you in order to best guide you. If the wife entered as a visitor and the husband is only a resident there are myriad possibilities: 1) if the husband could Naturalize, the wife might not need a waiver or go home; 2) if they married within 60 days of the wife's entry to the U.S. there could be preconceived intent issues; 3) if the husband petitions the wife but the husband cannot Naturalize, is there sufficient hardship to consider a waiver of unlawful presence inadmissibility?; 4) is there an unlawful presence inadmissibility? -- perhaps the wife has not been here over 180 days past the expiration of her authorized stay; 5) if the husband cannot Naturalize, might 245(i) eligibility come into play, permitting the wife eligibility to adjust status? I would recommend speaking with an experienced and reputable attorney, it looks like there might be some options for this husband and wife.
You may be able to do so, but it depends on many other factors. You can discuss this or other options that you may have with an attorney.
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