Where Is My Sent Message? - Shared Mailbox Sent Folders
When communicating from a shared mailbox, where the sent message is located depends on the version of Outlook that you're using.
Desktop Outlook
If you are using the old Outlook desktop application, then the sent message will save to the shared mailbox's Sent folder.
If you are using the new Outlook desktop application, then sent messages will save to your personal username@wwu.edu Sent folder.
OWA (Outlook on the Web)
If the shared mailbox is opened in a new tab, then any sent emails will display in the Sent folder of the shared mailbox.
If the shared mailbox is opened within the same tab, listed under your personal mailbox, and/or you are sending by changing the "From" field, then sent messages will appear in your personal username@wwu.edu Sent folder.