Go to Settings -> System mailbox and select a mailbox from the list:
Next, go to the Users subtab and add a user:
The user will see the system mailbox to which he or she has been assigned in their Mail tab:
After assigning the users to system mailbox, you can choose if you want:
them to have the access to the e-mails from this mailbox
to give them the permission to edit the system mailbox (for example to change the list of synchronized folders) by putting a tick next to Edit permission:
Remember to use the Save button to save the changes.