Which invention from the Industrial Revolution was the

most important and why?

Tough one. IMO

Telephone, communication was very difficult back then. The telephone made life easier for the rich (very expensive) to live their luxury. This large brick phone eventually evolved into the thing I'm writing on. A cell phone. The device that has changed the world forever.

This question is a bit opinion based, but IMO, Telegraph.

Explanation:

It shaped modern communications and computer code.