I am studying Ruth. I follow the progression of Boaz proforming the kinsman ’s part to redeem Ruth and raise up offspring for her dead husband. So now his name won’t be forgotten. So why is the son Obed accredited to Boaz in the geneology of King David? I thought this first son was accredited to the dead husband.

The child that is born from Yibum [redemption] is accredited to the deceased husband only in the sense that his/her good deeds are, in part, considered a credit to the deceased; this because his marriage to the mother was the reason for the Yibum and in this way contributed to the child's birth (Sefere HaChinuch 598).