Everyone has heard of “useful idiots,” a term coined decades ago and widely attributed to Vladimir Lenin, the leader of Russia’s Bolshevik Revolution, who promised to bring down capitalism from within. But the Muslim Brotherhood, a leader in the global Islamic movement, learned a lot of tricks from its old communist buddies, say those who have studied the organization. They, too, have learned how to borrow from within. The Brotherhood’s revealing document, “An Explanatory Memorandum on the General Strategic Goal for North America,” which was seized by the FBI in 2004, states that the brothers “must understand that their work...