If I create a new module in AMM 9.0.6 with any assignment and save it, it does not appear on the front end. After a lot of trial-and-error, I've found that if I disable AMM (or use the Switch to Core Module Manager button), reopen the module and save it, it will then appear. I can then edit and save the module through AMM without any issues. I'm not sure with what version this issue started - I've been updating the component as updates have come out, but I haven't created any new modules for a while.
Also, if "Show Switch" is enabled in the AMM configuration, there is no button to switch from the Core module manager back to AMM, so I have to manually change the option= in the URL to get back to AMM. I don't know if this is normal - I haven't previously used the Switch option.