While she cannot be deported back to Cuba, there is no requirement that she be allowed to adjust status either. It would depend if she qualifies for a Waiver. If not, she would need to get either criminal relief on the crime or a pardon.
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At first, you need an immigration attorney to determine whether this felony has any affect on your mother's eligibility to adjust. If yes, there is a range of post-conviction remedies that might be available for your mother. Pardon by the State Board of Pardons may be one of them.
Do you mean a waiver from the Federal government or a pardon from the governor? The pardon is a n uphill battle to get. The waiver she might be eligible depending on. Number of factors that cannot be determined on the facts presented
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There is a difference between being a refugee and a Cuban paroled in the public interest. Many Mariel Cubans believe themselves to be refugees, but their actual status is not that. If she was "paroled as a refugee" prior to April 1, 1980, then she is likely a refugee. If she entered after April 1, 1980, it is likely she is a parolee. This makes a big difference in terms of the types of waivers available and the types of crimes that result in potential deportation consequences. While it is rare, there ARE instances where Cubans are deported. You should NOT do this yourself. Your mother's status needs to be confirmed before you can even determine what her basis is for adjusting (getting residency). You need an immigration attorney. If your mother is a refugee, there is not application fee and a very generous waiver available. If she is a parolee, a waiver is available, but it is much harder. And she may or may not need a waiver. Do not do anything unnecessarily and retain an attorney before you take action. Far easier to prepare a good case than fix one that has gone bad. If you can afford it, consult with at least two attorneys. Similar advice you know is solid advice, differences are either differing strategies of individual attorneys or incompetence. Select one that makes you feel comfortable and lets you know what to expect, not one that tells you what you want to hear and/or gives you odds/guarantees. Good luck to you and your mom.