A week after the death of President Lorenzo Snow, the First Presidency was reorganized on October 17, 1901.
In A Comprehensive History of the Church 6:386, it states: "Joseph F. Smith was chosen president and selected John R. Winder and Anthon H. Lund for his counselors in the order named. John R. Winder at the time of being selected was second counselor in the Presiding Bishopric of the Church, a high priest, therefore, and a man of large experience, much beloved by the brethren of the authorities, and by the people generally. Anthon H. Lund was a member of the apostles' quorum and a faithful man, held in esteem everywhere and by all classes of the community."
The history states that President Smith, shortly after becoming president of the Church, spoke in a special general conference about the reason he, and President Snow before him, had reorganized the First Presidency relatively quickly. He said that when President Woodruff became the Church's leader, "he desired it understood that in all future time, when the president of the Church should die and thereby the First Presidency become disorganized, it would be the duty of the proper authorities of the Church to proceed at once without any unnecessary delay, to reorganize the First Presidency."