The help files aren't very specific about this, but apparently you're supposed to be able to hit the 'share' button in your missions journal to give the quest you're currently on to party members.
However, I was recently trying this with a duo partner, but it didn't actually seem to do anything. Nothing happened when hitting the button (other than the person hitting it got the 'SHARING MISSION: ' popups).
It didn't matter if we were right next to each other, who was leader, if we had appropriate empty mission slots, if we then took the mission manually but were on different steps....basically this thing didn't seem to do anything.
How do we actually get this working? Is there a restriction we were missing? What's it actually supposed to do?