When trying to add a mailbox to a mailbox collection, the mailbox is not displayed under the server, more can be found in the "all mailbox collections" within QMM.
One of the possible causes for this issue can be that the mailbox is hidden from the Exchange address lists.
To resolve the problem:
1) Connect to the source domain with AD Users and Computers.
2) Open the Properties of the user whose mailbox is not showing up as a server recipient.
3) Click on the Exchange Advanced tab and check whether the 'Hide from Exchange address lists' check box is selected.
4) If it is selected and you want to add the mailbox of this user to the mailbox collection, clear this check box.
5) Refresh the Exchange server in QMM Management Tree or add the mailbox to server recipients by right-clicking the server and selecting 'Add Recipients to Database' command from the shortcut menu.
After performing these steps the mailbox can be added to a collection for processing.