If your mother now is a Lawful Permanent Resident, then she will not become eligible to apply to become a naturalized citizen until 90 days before the end of five years from the date she became a Permanent Resident (90 days before the end of three years for many people who obtained their Permanent Resident status based upon marriage to a U.S. citizen). Your own status as a U.S. citizen will not alter this time requirement. Aside from the amount of time one must wait to become eligible for naturalization, there are many other details that determine eligibility. It would be wise for your mother to consult with an immigration attorney who, after learning all the relevant details about her, will be able to advise about eligibilities, options and strategies, and will be able to offer legal representation in the often quite complex naturalization application process.
If she has been a permanent resident (green card holder) for 5 years or more, has no criminal history and can pass the citizenship test and interview, she can file for citizenship. The only thing that you can do is make sure she can converse in English (does not have to be perfect English) and can pass the citizenship test.
If your mom has been a U.S. permanent resident for five years and has no criminal issues, she can apply to become a U.S. citizen. There is nothing you need to do; you do not "sponsor" her to become a citizen. She is the one who has to go through the naturalization process if she wants to become a U.S. citizen.
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