As far as I know, Resource mailboxes cannot be accessed directly using Outlook Web App or Outlook client. We can open a resource mailbox as a delegate's mailbox.
Assign Full Access permission for you to this resource mailbox and then open it via:
- File > Account Settings > Account Settings
- Double click your Exchange account.
- Click More Settings.
- Under Advanced tab, click Add and type resource mailbox.
Then you will see Inbox or other folders of this mailbox.

Same with shared mailbox.
Hope the information is helpful to you.
Regards,
Perry
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