(replying to orig so people don't have to scroll)
- Open File Explorer (easiest way is to hit the Windows {4 squares} button then type "File Explorer")
- In the left pane, right click on your OneDrive (in my case, it's named "MyName - personal")
- Scroll down to and click on "more options"
- Click on "Always keep on this device"
It'll take a minute or two to update all your files.
I'm sure there are better ways to make these files accessible without actually keeping them on the device, but I don't know how.