Way to unlock: Talk to Cullen in Skyhold after completing "Perseverance" task and talking with him in the armory, relationship with Cullen is required as well.
The quest-giver: Cullen (M12,7)
After completing the "Perseverance" quest you will find a note in Cullen office. He can be now found in the armory - go there to meet him - you will be able to change your decision about his addiction to lyrium.
After the cutscene go back to Cullen office. He will ask you to move with him to Ferelden - the quest will begin if you agree. You must be in relationship with Cullen to start this task. The whole quest is a cutscene in which Cullen will give you a memento coin - no matter if you decide to take it or not the quest will end in the same way.
No rewards for completing this quest.