I conpleted the BoZ collection on my main character Fairlyn, Maj'Dul server. Then I went to the status merchant and purchased the rewarded neck, Choral Collar of the Songster, for other characters on the account. Now, when I complete a weekly I receive a Fragment of Collected Ballads on the character that has already completed the collections and completely upgraded the green Spiritstone of Collected Ballads. I do not need that on this character but on the alt characters I purchased the neck for. Please see if the Fragment of Collected Ballads can be made available to the alt characters.
