One QuickSupport link add service case to all user group queue.

As I see, a QuickSupport add a service case in the Queue of the user who do the QuickSupport link (proprio). The Queue is updated to this user but not in the queue of the other users of the group added in the QuickSupport.  Is it possible to update the Queue of all the users so each user can see the case and chose to bring it and to solve it ?  To have a share queue for all the users of a group ?

Also, Why if I share a group, I can use the group in the QuickSupport I do but an other user can not use the same share group in a QuickSupport he do ? 

In this exemple of a QuickSupport:  I want the users in the group Community to see the service case on each of the users Service queue .  Not just in the Service Queue of Jean K.  Also the Community group can be use in the QuickSupport only by the group creator even if it is share.

Thank's for your help.