The Spirit World and the Redemption of the Dead

https://www.lds.org/study/manual/introduction-to-family-history-student-manual/chapter-9?lang=eng   

Very few will not accept the gospel. [9.4.3]

Some may wonder if many in the spirit world will accept the gospel message when it is presented to them. President Wilford Woodruff gave the following assurances:

“I tell you when the prophets and apostles go to preach to those who are shut up in prison, and who have not received the gospel, thousands of them will there embrace the gospel. …

“There will be very few, if any, who will not accept the gospel. Jesus, while his body lay in the tomb, went and preached to the spirits in prison, who were destroyed in the days of Noah. After so long an imprisonment, in torment, they doubtless gladly embraced the gospel, and if so they will be saved in the kingdom of God. The fathers of this people will embrace the gospel” (The Discourses of Wilford Woodruff, 152, 158).

During the October 1893 general conference, President Lorenzo Snow (1814–1901) shared similar thoughts:

“The great bulk of those who are in the spirit world for whom the work has been done will receive the truth. The conditions for the spirits of the dead receiving the testimony of Jesus in the spirit world are a thousand times more favorable than they are here in this life” (Millennial Star, Oct. 6, 1893, 718).

“A wonderful work is being accomplished in our temples in favor of the spirits in prison. I believe, strongly too, that when the Gospel is preached to the spirits in prison, the success attending that preaching will be far greater than that attending the preaching of our Elders in this life. I believe there will be very few indeed of those spirits who will not gladly receive the Gospel when it is carried to them. The circumstances there will be a thousand times more favorable” (Millennial Star, Jan. 22, 1894, 50).