I represented a mom and her son in a similar case. It wasn’t a donor situation but a one night stand. I’m pretty sure that there had been a blood test years earlier. We ended up with enough money to get the young man started in college. The father had known about this kid and had avoided being served etc. so the facts were different but we resolved it by having the money go to the son instead of the mother.
Judging by the boy’s age, it looks like her motive was to get him to pay for the boy’s college tuition