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The Stick of Judah And Joseph
Questions and Answers:

1. Why is the Book of Mormon called the Stick of Ephraim, when it is understood to have  been written by the descendents of Lehi who was a descendant of Manasseh?

"The  Book of Mormon refers to Lehi’s colony as made up of descendants of Manasseh and  Ephraim.  Lehi was a descendant of Manasseh, and Ishmael, of Ephraim.  There are promises in  the  Hebrew scriptures respecting Ephraim, which cannot be realized, so far as we know, except  through the seed of Ephraim dwelling upon the land of America.  
Since Lehi was of  Manasseh,  and Mulek’s colony were Jews, it leaves Ishmael alone to introduce the descendants of Ephraim into the western world.  The inter marriage of the families of Lehi and  Ishmael  effectually  accomplished this.
President  Franklin D. Richards, and other Latter-day Saints ac­quainted with the Prophet Joseph, have declared,...that in conversation they had known him to say that in Mormon’s abridgement of  the book of Lehi,
[which 116 pages of manuscript was lost by Martin Harris], it was  plainly stated that Ishmael was of the tribe of Ephraim."    
"It   is  well  known,  through  patriarchal  blessings, that many of the Latter-day Saints, in whose hands is the stick, are of Ephraim."  (Improvement Era, Vol 8, No. 10 Aug 1905 PP 782-782, by Joseph F. Smith)

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