If all their mail is already being managed via outlook, then all you need to do is connect to the exchange server in outlook, and move the messages from the local store to their mailbox. This can absolutely be scripted with the outlook.Application com provider.
$outlook = New-Object -ComObject Outlook.Application
$mailbox = $outlook.session.folders | ? { $_.Name -eq "your Mailbox name"}
$localstore = $outlook.session.folders | ? { $_.Name -eq "local folder name as it appears in outlook"}
$localstore.items | % { $_.move($mailbox)}
Obviously there is a lot of refinement required here, but it can be done!
~glenn