I say, and with God's success: It is not permissible for him to wipe over the socks; because it is a condition for the permissibility of wiping over them that there remains on each foot from the front of the foot in the sock the equivalent of three fingers from the smallest fingers of the hand; this is so that the required amount from the place of wiping exists. If it does not exist, it is not permissible for him to wipe, even if the heel of the foot is present. Refer to: Nihayat al-Mirad p. 380, al-Maraqiy p. 131, and al-Hadiyyah al-‘Alaiyyah pp. 39-40, and God knows best.