http://www.playonline.com/ff11us/cam...h/abyssea.html
Look at Gift 3:
[Gift 3] 1 Lunar Abyssite

"To use atma, you need lunar abyssite! It wouldn't do for us to give away atma and then not give a way to equip any, so we'll also present you with one lunar abyssite out of a possible three able to be carried.
* In the event that a character already possesses the lunar abyssite obtainable from certain NPCs, he shall receive 100,000 cruor instead."

I assumed that this is not exclusive to the Abysea noobs because it's not possible for them to have that Lunar Abyssite before even getting the add-ons. So how can we claim our cruor?