Short answer

Latter-day Saints and Muslims agree on the first half. Both say the message Jesus taught was changed after him. Latter-day Saints call this the Great Apostasy, and say Joseph Smith restored the true church. The Qur'an says Christians "forgot a good part of the message" (5:14). It says God (﷾) restored it through Muhammad (ﷺ), whom Jesus foretold (61:6). So the real question is which restoration holds up. A restoration must itself be kept. The Qur'an was memorised and written down in the Prophet's (ﷺ) lifetime, and it has not changed (15:9). Some of Joseph Smith's revelations were edited after they were first printed. The gold plates were taken back, so no one can check them. A restoration that needs restoring cannot be the last one.

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