"Óin , elder brother of Glóin, was one of the thirteen companions of Thorin Oakenshield on the Quest of Erebor. A skilled fire-maker, he failed to light one near the trolls when the group was captured. He dwelt at the Lonely Mountain until he accompanied Thorin on his great quest and journeyed into Moria with their kinsman Balin but was never heard from again.
The axe is found during the quest Vol. 2, Book 4 -- Instance: The Drowned Treasury
The axe is found and returned to his side during the quest Instance: Zigilburk Returned