From the Institute Manual:

John 14:16–23, 26; 15:26; 16:7. “Comforter” as a Title of the Holy Ghost and of Jesus Christ

In the New Testament, the Greek word paraklētos,translated “Comforter” in the King James Version, appears only in the writings of John. The word is composed of para, meaning “beside,” and klētos,meaning “one who is summoned.” A paraklētos is one who is summoned to another’s side as a helper, intercessor, or advocate. In John’s writings, the title paraklētos is applied to two individuals: the Holy Ghost and Jesus Christ. The Savior promised His disciples that after He departed, they would not be left alone but would have the companionship of the Holy Ghost to help them (see John 14:16, 26; 15:26; 16:7). The Savior’s promise that He would give His disciples the Holy Ghost as “another Comforter” (John 14:16; italics added) meant that He Himself was also a Comforter. The Prophet Joseph Smith spoke of the two Comforters in this way:

“There are two Comforters spoken of. One is the Holy Ghost, the same as given on the day of Pentecost, and that all Saints receive after faith, repentance, and baptism. This first Comforter [is the] Holy Ghost. …

“The other Comforter spoken of is a subject of great interest, and perhaps understood by few of this generation. After a person has faith in Christ, repents of his sins, and is baptized for the remission of his sins and receives the Holy Ghost, (by the laying on of hands), which is the first Comforter, then let him continue to humble himself before God, hungering and thirsting after righteousness, and living by every word of God, and the Lord will soon say unto him, Son, thou shalt be exalted. When the Lord has thoroughly proved him, and finds that the man is determined to serve Him at all hazards, then the man will find his calling and his election made sure, then it will be his privilege to receive the other Comforter, which the Lord hath promised the Saints, as is recorded in the testimony of St. John, in the 14th chapter, from the 12th to the 27th verses.

“Note the 16, 17, 18, 21, 23 verses. …

“Now what is this other Comforter? It is no more nor less than the Lord Jesus Christ Himself; and this is the sum and substance of the whole matter; that when any man obtains this last Comforter, he will have the personage of Jesus Christ to attend him, or appear unto him from time to time, and even He will manifest the Father unto him, and they will take up their abode with him, and the visions of the heavens will be opened unto him, and the Lord will teach him face to face, and he may have a perfect knowledge of the mysteries of the Kingdom of God” (in History of the Church, 3:380–81).