The complete letter has not been digitally transcribed and published online; the original manuscript page images are openly available from the Church History Library catalog at https://catalog.churchofjesuschrist.org/assets/a65137d7-083e-4784-8592-c99b42abc04f/0/4 ("Joseph F. Smith letter, Salt Lake City, Utah to Samuel Russell, Bern, Switzerland, 1901 March 19; Includes account of Joseph F. Smith's visit with David Whitmer in 1878"). A printed full transcript appears in Lyndon W. Cook, ed., David Whitmer Interviews: A Restoration Witness (Orem, Utah: Grandin Book Co., 1991), pp. 258–59.
The doctrinally and historically substantive core of the letter — Joseph F. Smith's recollection of his September 1878 conversation with David Whitmer concerning the signatures on the (printer's) manuscript of the Book of Mormon — is reproduced in Dan Vogel, ed., Early Mormon Documents, 5 vols. (Salt Lake City: Signature Books, 1996–2003), 5:47 n. 24, drawing from Cook 1991, 258–59:
I had the temerity to call the attention of Father Whitmer to the fact that the manuscript in his possession was but the copy of the original, and proved it to him by this circumstance: I asked him if he and the other witnesses each signed their own name to their testimony, and he unhesitatingly replied, "Yes, we each signed our name." Then I said, calling his attention to the names of the witnesses as inscribed in the manuscript, "how is it that all these names are written by one man?" He eagerly grasped the manuscript containing the testimony and glanced over the names. "Well," he said, "I don't know how this is, Oliver must have copied them." Still he persisted [in the idea that] it was the original manuscript, and not wishing to have an argument with him over the matter I let it drop.
The body of the letter also addresses (a) Smith's acknowledgment of Russell's letter of 29 October 1900 with enclosures, and (b) Smith's declination, on behalf of the LDS Church, of the proposal — conveyed by Russell on behalf of the Whitmer family / George W. Schweich — that the Church purchase the David Whitmer / Joseph Benjamin Whitmer manuscript material then held by Schweich (the printer's manuscript and related Whitmer papers, which the Reorganized Church of Jesus Christ of Latter Day Saints subsequently purchased from Schweich in 1903). See, on this point, Dialogue: A Journal of Mormon Thought 29:4 ("'White' of 'Pure': Five Vignettes"), citing the same letter.