Complex sentence: During the 1880s his conspiracy theories included the claim to have exposed the Jesuits as the assassins of President Abraham Lincoln, and that, if unchecked, the Jesuits could eventually politically rule the United States.
Split into simpler sentences: During the 1880s he claimed to have exposed the Jesuits as the assassins of President Abraham Lincoln. He also warned that, if unchecked, the Jesuits could eventually politically rule the United States.