Though the Lancelot section of the cycle has him converted by Joseph himself, the Estoire del Saint Graal section, written after the Vulgate Lancelot as a prequel, states that Joseph's son Josephus converted him.
Although the Lancelot part of the cycle indicates that he was converted by Joseph, the Estoire del Saint Graal section, written later than the Vulgate Lancelot, suggests that Joseph's son Josephus was responsible for his conversion.