To be able to send emails in Office 365 from a 'shared mailbox' you will need to ensure the user that is sending the email has permissions to send as the shared mailbox.

In the Office 365 Administration centre, you need to select the shared mailbox and edit the entry:

From the mailbox setup area, you need to ensure that user that is trying to send the mail from within the P11D Organiser is listed in group with privileges to send.

Once you have added the account to the members list you will have to navigate to the "Manage mailbox permissions" section and add the accounts to the "Send on behalf of permissions".