mom had tried to pass the border many times & was caught using someone else name and sent her back. can she be forgiven? can fix papers for her?

It will likely be difficult for you to have your mother come over as a permanent resident. A record of fraud or misrepresentation requires a waiver application based upon extreme hardship to a qualifying relative, and a qualifying relative is restricted to being a US citizen or permanent resident spouse or parent. She cannot waive through you. On the issue of her being caught many times trying to come into the US illegally, she would incur a “permanent” bar in which she would not be allowed to apply for any waiver for 10 years if she stayed in the US illegally for one year total on or after 4/1/97 and then left and tried to enter the country illegally on or after 4/1/97. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.