My mom got her Permanente green card a little over 10 years ago ( she was visiting me and stayed with me for a month till she got it and left back hom

Not likely. Once a Resident stays outside the US for more than a year, they have voluntarily given up the card/Residency.  There are exceptions if she can show compelling reasons why she stayed. However, that would be difficult since it has been 10 years. There are also exceptions for military travel. Thus, it is likely that you will need to refile for her. She can try and enter, but it is likely she will be denied entry and returned home. Thus, you will need to file a new I-130 for her. She may also try to keep it by applying for a Returning Resident Visa at the US Embassy directly (see first paragraph). Feel free to email or call if you have any further questions: Harun@ksvisalaw.com