Hi Dsimmons,
I’ll give the following information for your reference:
1.When you give permissions to a DG, please make sure the DG is a security DG. To create a security distribution group, please refer to Create a Security-Enabled Distribution Group.
2.Give the DG FullAccess Permission of the shared mailbox
3.Give the DG Send As permission of the shared mailbox.
You can refer to the following article to give the DG permission:
Set Up a Shared Mailbox
4.Try to open the shared mailbox in Outlook Web App using the membership accounts of the DG.
To add the shared mailbox in one user account, please refer to the following steps:
1. Open Outlook Web App
2. Right click the name of the mailbox, and select Open Other’s Inbox
3. Enter the shared mailbox name you want to open
4. The share mailbox will appear under your mailbox.
Please note: It may take up to 60 minutes until users can access a new shared mailbox or until a new security group member can access a shared mailbox.
Thanks,
Vivian Wang