Armor MQs Between Characters on a Single Account

[jabic]

This question refers to Thurgadin quested armor. Please assume that both characters have the necessary faction to do the turn-ins.

Characters A and B are on the same account. Character A has a piece of corroded armor, Character B has the three corresponding gems for that piece of corroded armor. Character B wants to get the rewarded piece of arm.

Character A turns in the piece of corroded armor. Character A logs off. Character B logs in and turns in the corresponding gems immediately. Will Character B get the reward?