I couldn't get this working initially, but it turned out that I had to set the path to IE's executable manually. Even though in the add-on's settings it says that the correct path (for Windows users) is automatically set if you don't manually type in a path, for me this didn't work. I had to manually set the path as the following: -

C:\Program Files\internet explorer\iexplore.exe

Once I'd done that, it started to work just fine.

I've knocked a star off because of the issue mentioned above and because of having to install an extra process to get this to work. While I get that the latter is a limitation of Firefox's new add-ons system, it's still off-putting from a security standpoint.

Many thanks to the developer for both this add-on and the "Open in Microsoft Edge" one, which worked fine without me having to set the path manually.