I've a trouble with sending email on behalf of by using my personal account and a shared mailbox in which the autorization "on behalf of" is my account.
In the "from" field of outlook I've added the shared mailbox. But the email was send as shared mailbox not on behalf of. So I've tried to add "delegate access" to the shared mailbox but nothing changed.
If you have both Send As and Send on behalf of permissions granted, the former takes precedence when sending. You can work around it by adding the shared mailbox as an additional account (via File -> Add Account) and using the "send using" dropdown menu when composing the message. I've put some details and screens about this here: https://www.michev.info/Blog/Post/1430/send-as-send-on-behalf-of-and-permutations