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“There is a difference between the Holy Ghost and the gift of the Holy Ghost. Cornelius received the Holy Ghost before he was baptized, which was the convincing power of God unto him of the truth of the Gospel, but he could not receive the gift of the Holy Ghost until after he was baptized. Had he not [been baptized], the Holy Ghost which convinced him of the truth of God, would have left him.” — Joseph Smith, Jr.
There is a difference between the Holy Ghost and the gift of the Holy Ghost. Cornelius received the Holy Ghost before he was baptized, which was the convincing power of God unto him of the truth of the Gospel, but he could not receive the gift of the Holy Ghost until after he was baptized. Had he not [been baptized], the Holy Ghost which convinced him of the truth of God, would have left him.