The issue seems to occur because of the original PST file was residing on a network drive.
The problem is - if you attempt to open Outlook when the default PST file is unavailable (e.g. because the network drive takes too long to establish itself), Outlook will create a new default PST file having the same name.
In this case, this new PST file somehow acquired a password. I suspect when it happened, my wife was prompted whether she wanted to set a password for the new file, and entered something not realising what she was doing.
In any case, going into Control Panel and editing the Outlook mail settings from behind the scenes to set the original PST file as the default cured the problem.
To get to these settings, go to Cortana and enter 'run'
Then enter 'control' to run Control Panel.
In 'Search Control Panel' enter 'mail'
And launch 'Mail (Microsoft Outlook 2016) (32-bit)'
Select 'Data Files' and change the settings to point Outlook to the correct PST file.
You may fine a new, very small Outlook PST file on the local drive having the same name as the original PST file.
Once fixed, run Outlook and it should launch as normal.
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