1,  Open Registry.
2,  Navigate to [HKEY_CURRENT_USER\Software\Microsoft\Office\15.0\Outlook\Profiles]
3,  Export the whole profiles to file
4,  Make sure know where your PST file is located and have a backup of it.
5,  Backup Done

On re-install of outlook 2013

1,  Open Outlook for the registry keys to be created along with a new pst file and close outlook
2,  Navigate to the new pst file and delete it.
3,  Re-Open Outlook, it will complain about the pst file being missing but just point it back to your original pst file.
4,  Close/Re-Open outlook to ensure it is using your old pst file and close outlook again.
5,  Import the exported registry profiles.
6, Open outlook, Send/Receive and re-input all your passwords and click the save (if you wish for them to be saved)
7, DONE