Final answer:
The influential church leader whose telegram inspired a song is Dwight L. Moody, known for his evangelical preaching and revivalism in the 19th century.
Step-by-step explanation:
The great leader in church extension whose telegram to Robert Ingersoll inspired a song is Dwight L. Moody. His telegram to Ingersol was in response to a public challenge from Ingersol, who was a prominent agnostic and critic of Christianity. Moody's telegram, which simply said 'I still believe', inspired a song called 'I still believe'.
Dwight L. Moody was a preeminent evangelical preacher and leader in the 19th century. He was known for his urban revivalism, social outreach, and inspiring messages which resonated with a wide audience, leading to a profound impact on both American Christianity and the international evangelical movement.