From the old system logged in as the user...
- Locate their Firefox profile folder
- Open Explorer and browse to %APPDATA%\Mozilla\Firefox\Profiles
- Right-click on their profile folder (e.g. xxxxxxxx.default), and select Copy
- Right-click the backup location (e.g. a USB-stick, a blank CD-RW disc or network location), and select Paste
From the new system logged in as the user...
- To restore the old profile on the new system
- On the new system, open Explorer and browse to %APPDATA%\Mozilla\Firefox\Profiles (they need to have opened Firefox at least once)
- NOTE the name of the profile on the new system...copy the name to a text document
- Copy the old profile to the %APPDATA%\Mozilla\Firefox\Profiles location on the new computer
- Delete the new profile and rename the copied one to the same name as the deleted one
- Opening Firefox should correctly use the copied profile