Use the latest Fractal-Bot to update the firmware and then update Axe-Edit III. You can't update firmware from Axe-Edit III -- you do it from Fractal-Bot.
The editor for the III is called Axe-Edit III, not Axe-Edit. This allows both editors to co-exist peacefully on one machine. You can even run them both at the same time with both a III and an older II unit connected and active at the same time. Additionally, you can run an AX8 and the AX8-Edit in parallel as well. Makes it easier to maintain multiple units, copy things from one to the other, etc.