So your mother's son is the eldest and only male in your family.
I presumed that the HDB flat was originally purchased in the joint names of your parents, and when your father passed away the HDB flat became fully owned by your mother by the operation of the law of survivorship in joint tenancy. At that point, the HDB flat was not fully paid yet, and your mother, who wasn't working at the time, needed an injection of CPF funds to continue servicing the HDB mortgage.
Your mother effected a transfer of the HDB flat to your mother's son and herself, again in joint tenancy, so that she could use the son's CPF monies to service the monthly loan repayments.
Tio boh ?