We have Advanced Module Manager Pro installed and there is perpetually an extension update available for Advanced Module Manager (not pro). They are both 9.3 but it appears AMM update will overwrite AMM-Pro.
That is weird.
If you have the Pro version installed, you should not be able to install the Free version over the top of it.
The installer should break the process off with a message like this:
See if you can do a rebuild on the Update Sites. Does that solve it?