The following article should walk you through setting up the notebooks on the computers.
Use a notebook on multiple computers
After setting up notebooks on multiple computers, there is a fairly common question that gets asked. What happens once the connection is lost (which can happen for various reasons)?
The article briefly describes what happens "OneNote creates an offline copy on that computer. Thereafter, whenever OneNote is open on that computer and the computer is connected to the shared location, OneNote continuously synchronizes and merges the changes to the notebook from each computer."
How this works is that on each machine that OneNote is installed, a cache location is created. Everything you type, insert or create in OneNote will automatically get saved to this location first. This happens behind the scenes and is the reason that from the UI (User Interface) perspective, you don't need to ever click on Save. Where this comes in useful is that if (more likely when) you lose your connection to the shared location, you will still be able to work in OneNote. Once the connection is restored OneNote will sync those changes back to the shared location, all without you knowing or having to worry about it.
Author for the post: - Brandon Desjarlais
"Once the connection is restored OneNote will sync those changes back to the shared location, all without you knowing or having to worry about it."
I'm about to ditch OneNote because it often does *not* do this, and I can't find any hints on what to do to improve this, despite many hours of searching.