Hi, Vendithià! o/
If I understand this correctly, you activated the device, and killed the elemental appearing, but the quest didn’t advance, and is still asking you to activate the device, right?
If this is the case, I would simply abandon the quest and start it again. You’ll have to kill the elemental again, but it should work.
What probably happened is that at some point, while playing with your friend, your group became a raid group. Most quests can’t be completed in raid groups, which can cause these kinds of issues.