A shared or delegated mailbox is different from your own Office 365 account, it's a second mailbox (a team inbox, a manager's calendar, a departmental address) that your Exchange admin has granted you permission to access, on top of your normal login.
What BlueMail signs in to
BlueMail works with mailboxes that have their own email address and credentials, which is what lets it keep each account fully independent, its own sync, notifications, signature and color. Give BlueMail a sign-in and it will treat that mailbox as a first-class account.
That is the key to shared and delegated Office 365 mailboxes too: where access is granted only through your personal login, the mailbox has no sign-in of its own yet, so the fix is to get it one, which is the first option below.
Your own Office 365 account still works as usual: BlueMail can auto-detect it as a device account, or you sign in through the Microsoft consent screen. See Adding an Exchange Account for the setup steps.
Your options instead
- Ask your admin whether the mailbox can have its own sign-in. Some organizations enable direct sign-in on a shared mailbox, giving it its own password. At that point it is effectively an individual account, and you can add it to BlueMail the normal way: Settings | Accounts | Add Account, entering the shared mailbox's own email address and credentials.
- Use Outlook or Outlook on the web for the shared mailbox. Delegated access without separate credentials is a Microsoft-side feature, and Microsoft's own apps are where it works. You can keep your personal account in BlueMail alongside.
Check with your admin
Because shared and delegated mailbox permissions are configured on the Exchange/Office 365 side, your IT admin is the best source for confirming exactly what access you have and whether the mailbox can be given its own sign-in.