The Saarthal Amulet does not show up in the inventory

Well, I cured my own lycanthropy. I noticed there is one vote on this so I am sure that there are people who are still interested in this. I will leave as much detail as possible in the hope of helping people who have this issue in the future.

First of all, yes, the process for curing is exactly the same as how you cure Kodlak. You just have a witch's head in your inventory and examine that blue flame where you fought Kodlak's beast, and the option pops up, something like "Toss a head in the fire and cure your lycanthropy forever?"

Now, this is about the 300th time I'd tried activating that thing, so there is just some serious bug going on here. I think it's probably related to the fact that I spammed that flame the first time I was there during Kodlak's quest.

Here is the circumstance under which it finally worked:

To get the "purity" quest, continue doing random "quests" for Farkas and his brother until they tell you that they want to cure themselves.

I did Farkas and even though I used the flame to cure Farkas, I never got an option to cure myself. Then I did the same thing with his brother. When you have this quest, activating the blue flame causes the beast to come out right away.

After this, I tried to activate it, but nothing happened. Then I spoke to Vilkas and he said something like "Thanks, now I'm going to stay here for a while." After that, I tried the flame again and it worked.

I don't know if it finally working was related to what my actions were or whether it was just some random chance, but know that there is hope for those who think they will be stuck as a werewolf forever. Good luck.

Check your key-bindings. Also be careful about where you store items. I believe that items can disappear if you store them in random barrels, and sacks. The safest way to store items are in containers in your own home.