By properly performing vicarious ordinances in holy temples, we help rescue the qualified deceased souls who otherwise would not be able to receive the ordinances of salvation and have full access to the blessings of the Atonement of Jesus Christ.
58 The dead who repent will be redeemed, through obedience to the ordinances of the house of God . . .
Elder Tad R. Callister wrote:
“On October 3, 1918, President Joseph F. Smith sat in his room pondering the scriptures and reflecting on the great atoning sacrifice of the Savior. He was impressed with Peter’s account of the Savior’s visit to the dead (1 Peter 3:18–20; 4:6). While so meditating, the eyes of his ‘understanding were opened’ (D&C 138:11) and he saw the hosts of the dead of whom Peter spoke. He perceived that the Savior organized His missionary forces and sent them forth to preach the gospel to those who had not yet heard its glorious truths. In unmistakable language, President Smith reports that the redemption and its effects were taught to those earth-departed spirits: ‘There he [the Savior] preached to them the everlasting gospel, the doctrine of the resurrection and the redemption of mankind from the fall, and from individual sins on conditions of repentance’ (D&C 138:19). . . . In verses 29–32 of this same section, President Joseph F. Smith makes it clear that it was not the Savior who personally preached the gospel to the ‘wicked and disobedient’ but that He ‘organized his forces’ among the righteous and sent them forth to preach. . . . Then follows this conclusive pronouncement of President Smith: ‘The dead who repent will be redeemed’ (D&C 138:58). The Atonement was and is being taught to the dead, and furthermore, it is efficacious for those among them who choose to repent.”
(The Infinite Atonement , 79–80, 82.)