desaiv

My mother has a greencard and she came to the US and then had to leave to go back to India for some family work. However, after she reached India she saw her passport and saw there was no stamp upon her arrival in Atlanta. So when she comes again, how would the immigration officers know when she was in the US? Would they be able to get this information from their computer (I am guessing they swiped her greencard)? My fear is when she comes next year, they won't have a record of her coming here this year since her passport contains no stamp. She does have her boarding passes to show for. TIA for any help in this matter.