Question
Where can I find emails sent from a Resource Account's mailbox?
Answer
In the Outlook application, any emails sent from a resource account's mailbox will end up in the Sent Items folder of the individual who sent them--not in the resource account's Sent Items folder.
The only way to have those emails end up in the Sent Items folder of the resource account is to send emails from the resource account while in OWA (known as either Outlook Web App or Outlook on the web).
Microsoft has more information regarding this behavior.