Finlayson went on the national transplant list last year, but the odds of her getting an organ looked pretty slim.
Her son, Brandon, was a match and volunteered to be a donor.
"She pretty much shut us down and said, 'No, it's not a possibility. I don't even want to talk about it,' " Brandon, 37, said. "It took days to get her to finally even think about the idea. A lot of convincing."
"Normally we take the right lobe and take about 60 percent of the healthy liver from the donor to give to the recipient," said Dr. Manuel Rodriguez-Davalos in a statement.
Doctors said that Gwen and Brandon's livers can regenerate and should grow to about 90 percent of normal size within months.
"I look forward with joy and optimism and try to figure out what are we going to do next."
"I'm not sure I have the words to describe how I feel about my son. I am grateful that he is the kind of man who would do something like that," she said. "That he would risk his life for another human being -- didn't have to be his mother -- it would have been anybody. To me, that is the definition of a hero."