I have brought forth some more information for you guys!

Will Ifrit/Moogle/Garuda weapons and unique/untradable gear from instanced raids be storable?
The unique/untradable storage box is generally reserved for items that can only be obtained through events and other gear that cannot be obtained more than once. As such, items such as Ifrit weapons and Moogle weapons can be obtained more than once, and therefore aren’t storable.

We will have a Topics article regarding the item storage box soon, so please hang on for more details.