Final answer:
Elijah Muhammad was the leader of the Nation of Islam, which Malcolm X was a part of before he left to form his own organization and was later assassinated by NOI members.
Step-by-step explanation:
The leader of the Black Muslims, formally known as the Nation of Islam (NOI), during the critical period of the civil rights movement was Elijah Muhammad. Malcolm X, born Malcolm Little, was a prominent figure within the NOI and became well-known for his fiery oratory and advocacy for black empowerment under Elijah Muhammad's leadership. However, Malcolm X later dissociated from the NOI, creating his own organization with different ideals before his assassination in 1965 by members of the NOI.