In order to log an email from your Outlook account to a shared mailbox that you have access to, you will first need to add the shared mailbox's email address to your Acceptable Email Addresses list in Salesforce settings. Here are the steps to do so:
1. Go to “Settings” (this is under the little bear figure in the top right corner)
2. Search “Email” in the Quick Find box and select “My Email to Salesforce”
3. Look for the My Acceptable Email Addresses section:
4. Put a comma after your email address and then add the email address for your shared mailbox.
5. Select “Save” at the bottom