Can Mary apply for citizenship three-year after getting the conditional green card or the permanent green card ?

She must be a lawful permanent resident for three years to apply for naturalization. She would use the resident since date on her lawful permanent resident card (which should be the date she became a conditional resident) to calculate her third anniversary. She must meet all other requirements to naturalize under the three-year rule. You can read more about naturalization at http://myattorneyusa.com/citizenship-and-naturalization.