Have a fresh Exchange 2013 install and have configured and setup shared mailboxes for the users. Users have to be a member of specific security group to be given permission to attach the mailbox or send as the attachable mailboxes address.
The problem occurs when User A has an attachable mailbox (Mailbox 1) and creates a fresh email to be sent from the Mailbox 1 email address - it just gets stuck in User A's outbox. However, if User A was to reply to an email in Mailbox 1 the email would send just fine!
I'm starting to suspect this is a permissions based problem but I've been over the active directory settings and the settings in the ECP and they match other working shared mailboxes.