When you speak to the NPC in charge of hunting task rewards he informs you: Walter Jaeger: Please note, that all items will be put into your Store inbox! This means rewards can't be traded or destroyed. So you cannot share any item with another character for their house. Additionally, hunting task points are based on the individual character not all the characters on the account. For example, if you want the Falconer outfit on all of your characters you need to earn points on each and every single character on your account as rewards/points don't apply to all your characters.
Signed,
Your Feared Bountyhunter.