"Who has the mantle of the prophet today? (The current President of the Church.) How is this mantle transferred when the prophet dies?"

President Joseph Fielding Smith explained:

"There is no mystery about the choosing of the successor to the President of the Church. The Lord settled this a long time ago, and the senior apostle automatically becomes the presiding officer of the Church, and he is so sustained by the Council of the Twelve which becomes the presiding body of the Church when there is no First Presidency.

"Did Joseph Smith ordain any man to take his place. He did. Who was it? It was Hyrum, but Hyrum fell a martyr before Joseph did. If Hyrum had lived he would have acted for Joseph" - Brigham Young (Times and Seasons, 5 [Oct. 15, 1844]: 683).

Following the principle of lineal succession, Smith's younger brother Samuel was the next potential candidate in line. Sometime between June 2327, 1844, Smith reportedly stated that "if he and Hyrum were taken away, Samuel H. Smith would be his successor" (Smith, An Intimate Chronicle, p. 138; William Clayton Diary, typescript, 12 July 1844, original in First Presidency's Archives)- Wiki Succession Crisis

The sole remaining Smith brother, William, charged that Brigham Young had arranged for Samuel to be poisoned to prevent his accession to the presidency. Others attributed Samuel's death to an internal injury sustained during his retrieval of the bodies or to illness. William Smith's charges were not considered sufficiently well founded to merit pursuit by legal authorities. - Wiki "Samuel_Harrison_Smith"

"laid hands upon bro. Sidney [Rigdon] and confirmed upon him the blessings of wisdom and knowledge to preside over the Church in the absence of brother Joseph" (Joseph Smith Diary, 19 April 1834, Church Archives; Jessee, Papers of Joseph Smith, vol. 2, pp. 3132).

"Immediately after the martyrdom of Joseph, John Taylor, Willard Richards and William W. Phelps took a kind of temporary direction of the affairs of the church, instructing the saints to wait patiently the hand of the Lord; assuring them that he had not left them without a shepherd, and that all things would be made known in due season. To every question of the saints, Who is the prophet? replies were made, in substance, that the saints would know in due season, but that nothing could be done until the Twelve got home, because the appointment of a prophet and the directions for salvation of the church from the perils they were in, was contained in sealed packages directed to them. Orson Hyde and others of the Twelve, who were then in the east, stated in public congregations in New York, Philadelphia and other cities, that Willard Richards had written to them that the appointment of a prophet was left with him, under seal, to be opened on the return of the Twelve. This assertion was so often made that the whole church were daily expecting to hear a new prophet proclaimed. On the 8th day of August, 1844, when Sidney Rigdon endeavored to obtain authority to lead the church, John P. Green, marshal of the city of Nauvoo, told them, 'They need not trouble themselves about it, for Joseph had appointed one James J. Strang, who lived up north, to stand in his stead.' The sudden death of John P. Green immediately after this declaration (under very extraordinary circumstances) left Willard Richards and John Taylor sole repositors of all documents on this subject, except this letter." - Strang (1848), pg. 4.

The Presidency was then reorganized, following a precedent well established through generations of the past [this precedent is explained in the preceding statement by President Joseph Fielding Smith]. There was no campaigning, no contest, no ambition for office. It was quiet, peaceful, simple, and sacred. It was done after the pattern which the Lord Himself had put in place" (in Conference Report, Apr. 1995, 92; or Ensign, May 1995, 69).

How did the people respond when they saw Elisha duplicate Elijah's miracle of parting the waters of Jordan? (See 2 Kings 2:1415.) Why is it important that we immediately accept and sustain a newly ordained President of the Church? (See D&C 43:23, 7.)

What did Elisha say to the people when the 50 men came back without finding Elijah? (See 2 Kings 2:18.) What can we learn from the experience of the 50 men? (We should follow the counsel of the prophet the first time we hear it.)

Testify that the President of the Church is a prophet of God. Encourage class members to sustain new Church leaders and to follow the counsel of the prophets.