It sounds like she is a permanent resident. If so she should apply for naturalization.
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Please schedule a private consultation with an immigration lawyer. There are many details over a span of decades that have been left out in your question.
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How old was she when her father naturalized? Also, I agree with my colleague, sometimes the easiest route is just naturalizing from permanent resident status rather than trying to prove derivative citizenship. Another route is simply apply for a passport and sending in all the documentation they request for foreign born individuals.
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