The fix had to be applied in PowerShell for Exchange
As I didn’t know what to expect with changing from a Shared to a User mailbox, I firstly exported their mailbox as a PST.
New-MailboxExportRequest -Mailbox UserName -FilePath \\fileserver\share\username.pst
I ran get-mailboxexportrequest to check the progress of this. Once completed, I ran
Set-Mailbox -Identity "UserName" -Type Regular
to convert the mailbox type to a User Mailbox.
I checked Exchange Management Console and it now reported the user as having a user mailbox. The user reopened Outlook and everyting continued to work as normal, so the backup of the mailbox was not needed (this time).