Wylandriah's Spoon belongs to Wylandriah, a Bosmer court wizard. The spoon may be found at the town of Ivarstead inside Fellstar Farm. When entering the farm, look for Wylandriah's Satchel, which is sitting on a table in the far left of the home. The spoon is found inside the satchel.
Wylandriah's Spoon is a quest item and part of the "Hunt and Gather" quest. Once the quest is completed, Wylandriah takes the spoon from your inventory. After the item is removed from your personal inventory, it is no longer retrievable. Attempting to pickpocket Wylandriah will be unsuccessful if trying to reclaim the spoon (she will not have it on her).
If you desire to keep the spoon to add to a personal collection, you can simply kill Wylandriah before completing the quest. The spoon will now become a non-quest item, allowing you to store it anywhere.