How should I travel with a new computer monitor in its original packaging?

I just bought a new computer monitor for my nephew, and he's planning to travel back to the Bahamas with it. The monitor will stay unopened in its original packaging, which has the following dimensions: 11 inches wide, 19 inches tall, and 36 inches long, and it weighs 25 lbs.

It’s too big to be a carry-on, so I’ll have to check it in. Do you think the original packaging will be sufficient protection, or should I add extra padding around the box? Any tips on how to make sure it arrives safely?