Is their outlook getting mail from their exchange or do you have an IMAP configured to get VM's from CUE?
"I tried to setup their UC imap account in Outlook and autoarchive/delete after 5 days but it does not work with their Outlook. That method works on my personal computer."
What are you using on your computer that makes it work?
This thread may have some good info-
https://supportforums.cisco.com/thread/2024040?tstart=15
Thanks,
Anthony