As other comment says, it disappears from quest tracker when you loot the boss. If you mouse over Grand Warlock's Amulet it tells you that you use the amulet to get the fel ember out of a brazier in the Nethekurse's room.
Quest
How to Save a Life
A World of Warcraft quest in The Shattered Halls. Facts and objectives from the current retail game data.
The highest voted Wowhead comments for this page. They are community notes, not TheWoWDB comments.
[npc=16807] drops [item=23735]. In the same room as the boss, there are two braziers with purple flames on either side of the throne. They do not have any kind of mouseover tooltip, but stand next to one, and click the [item=23735] in your bags, and you'll get a [item=23726], which you turn in to the questgiver who catches up to you at the end of the dungeon.
However, if you're reading this, chances are good you did what I did: cleared the whole dungeon first and had one quest that you couldn't turn in. In that case, just pull up your map and run all the way back to "Throne of the Damned" and the first paragraph will make a lot more sense. From there, you can turn the quest in at the beginning of the dungeon, rather than run all the way back to the end.
The quest item used to gather the Fel Ember doesn't always show up in the quest tracker.
If you get stuck; check your bags!
Quest facts
The client quest POI data records no map location for this quest, so no map is shown.
Check whether you have already completed this quest
in-game: /run print(C_QuestLog.IsQuestFlaggedCompleted(29649))
Requirements
Read from the Blizzard quest API.
Description
Gunny is dying from a powerful curse, {name}. Grand Warlock Nethekurse augments his power with a pair of mystical braziers. If you bring me an ember from that brazier, perhaps it can counteract the dark magic?
Getting there
Inside the dungeon: The Shattered Halls
At the heart of Outland's barren Hellfire Peninsula stands Hellfire Citadel, a nearly impenetrable bastion that served as the Horde's base of operations throughout the First and Second Wars.
Bosses in the Adventure Guide, in order: Grand Warlock Nethekurse, Blood Guard Porung, Warbringer O'mrogg, Warchief Kargath Bladefist.
Entrance: Hellfire Citadel, Hellfire Peninsula at 47.4, 52.0.
Instance text, bosses and entrances are the client’s Adventure Guide data.
Community notes from Wowhead · 14 comments
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Reward details
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Reputation: Honor Hold +250
Vestiges of the Sons of Lothar, veterans of the Alliance that first came into Draenor, have steadfastly held on to this Hellfire outpost. They are now joined by the armies from Stormwind and Ironforge.
Reputation group: The Burning Crusade.
Other quests in The Shattered Halls that reward Honor Hold reputation: Revered Among Honor Hold (+250), WANTED: Bladefist's Seal (+350), WANTED: Shattered Hand Centurions (+250), Fel Ember (+250), One Last Favor (+250), Turning the Tide (+500).
Item facts are the current retail client’s (ItemSparse); the specialisations for a pick-one item are the ones the Blizzard quest API lists; faction and currency text is the client’s own. Lowest listed price = the US commodity auction house now.