I know That my Redeemer Livith, author: G. F. Handel
This Web site lists three similar versions: Resurrection and Easter Hymns and Songs:
* "I Know That My Redeemer Lives," words: Charles Wesley, music: George F. Handel.
* "I Know that My Redeemer Lives," words: Samuel Medley (1775), music: Duke Street, attributed to John Hatton (1793).
* "I Know That My Redeemer Liveth," words: Jessie Brown Pounds (1893), music: James H. Fillmore (1893)
#1, even the version you cite, Handel was behind the music -- he didn't author the text.
#2 - even the Mormons say the version they embraced, Samuel Medley was the author: History of Hymns—The Evolution of LDS Hymns:
Episode 13: The history behind "I Know That My Redeemer Lives": Samuel Medley, who wrote the text of “I Know That My Redeemer Lives” in 1775, was born in Cheshunt, England, just north of London, in 1738. He practiced sinful and profane ways until his leg was wounded in a naval battle in 1759. The possibility of amputation led Samuel to pray, asking that he might keep his leg. The prayer was answered, and Samuel Medley repented and lived for the Lord. Latter-day Saint Lewis D. Edwards wrote the melody we now associate with this hymn. This program includes contemporary renditions of the hymn by the following artists: the Gibbons Family, Michael Dowdle, Jenny Frogley and David Betros, Beverly Hansen, Greg Hansen, and the Brigham Young University Singers.