You are not able to move the password manager in Firefox. It should appear on left side of the address bar when Firefox detects that you are logging into a website.

As long as the Remember logins for sites option is selected in the Privacy settings of the Firefox options, then the password manager should function.

However, it is important to note that the password manager may not function on all websites. Firefox has different conditions to determine when you are logging into a website and some websites will not trigger these conditions. Also, some websites may allow Firefox to save the password, but may prevent Firefox from pre-filling the password into the login page.

Saved Password Editor {web link} Adds the ability to create and edit entries in the password manager.

There are some web pages that do not allow browsers to record or fill in the log-in information. You can try a Form Filling add-on.

https://support.mozilla.org/en-US/kb/how-to-fix-preferences-wont-save

Note: Some software, like Advanced SystemCare with Surfing Protection, can protect files in the Firefox profile folder against changes. If you have such software then check the settings or uninstall this software.