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The Transfiguration was a time for God to show the disciples they would know God’s desires by listening to His Son, Jesus Christ. Moses’ and Elijah’s presence was indication the time of the Law and the Prophets were nearing an end and Jesus was the fulfillment of both. The transfiguration had nothing to do with the transferring of the priesthood.
Indeed, it was a time to show the three men the glory of God while at the same time showing His Son is serving in humility! Why would God take away the keys of the priesthood from His ONLY Son and give them to man, who is fallible?
The Transfiguration too was a time to show the disciples the ultimate fate of Jesus; the resurrection, ascension and return of Jesus. (See Holman Bible Dictionary, Easton’s Bible Dictionary, Strong’s Concordance and Matthew Henry.)
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“Within a week of that promise, Jesus took Peter, James, and John to a high mountain, where keys of the priesthood were bestowed upon them, under divine direction, by Moses and Elijah (Elias). (See Matthew 17:1-5.) The Master then reminded his disciples of their sacred calls to the holy apostleship: “Ye have not chosen me, but I have chosen you, and ordained you.” (John 15:16; see also D&C 7:7.) Jesus not only called and ordained men, but he also taught them their duties.” Russell M. Nelson, The Power within Us. Salt Lake City: Deseret Book Co., 1988, 103.