Please explain the problem in detail.

I can save a password. I opened: 1) Tools. 2) Options. 3) Security. 4) Logging. 5) Remember passwords for sites. The option (Remember passwords for sites is not highlighted) and does not support activate (X)

I can not enter new passwords. No problems with the old.

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Go to that message, and use the Undo link to its right.

You may be in Private Browsing mode or told Firefox not to remember.

Type about:preferences#privacy<enter> in the address bar.

The button next to History, select Use Custom Settings.

Turn off Always use private browsing mode

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.