As suggested by the support I'm making a post here:
I crafted all the required amulets for the quest but the quest is not counting them properly:
-The Sphene Amulet worked just fine. It is also the only one I crafted not +1 on the first try
-The Silverspruce Amulet worked at first, but when I moved it in my bag it didn't count for the quest anymore
-The Rubellite Amulet never counted at all
I tried moving the +1 amulets to another characters to see if they were blocking somehow the quest but it didn't work. I also tried moving the correct amulets to another character via bank and back but it didn't work. The Sphene Amulet was considered crafted by the quest during all these tries.
I mailed them to myself and it fixed the issue, somehow (I got the idea while writing this post).
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All items submitted as quest turn-ins must be non-plusOne items (either as a crafting result, or by exercising the option to convert the item from +1 to normal (as an option/right-click selection). The ability to convert was added 9 months after mod 15 introduced the +1 items. Despite requests from the user community to correct the quest givers/NPCs, they remain as they were pre-mod15/Nov2018.
The OPs problem sounds like an item number mismatch issue. If the conversion from +1 to normal did not create an item identical to what is expected by the NPC it will be rejected.
That either the NPCs accept the +1 items as well or they can be converted?
It is quite hard / expensive / time consuming to craft all those items for masterwork IV with a lot less than 100% proficiency.
At least for me it is. So most of my tries are either fails (at "officially" around 80%) or +1 (at about 34%).
The normally highly coveted +1 item is suddenly useless and cannot be made useful. Which makes it very depressing. Especially as most of them needed drops from FBI Bosses/chests which also does not happen that often..
It was even more annoying after I needed up to 9 tries for +1 tools with more than 80% focus... But that's another story, just my bad luck.