Problem assigning a task to a specific group

Problem assigning a task to a specific group

 
Hi team,
 
     We are having issues assigning specific tasks to a specific group created or added to a request.  It only shows the group the requester belongs to.  The screenshot is below. 
 
 
     We tried creating or customizing a task template specifically created for a given task to that's already pre-assigned to a group but when we chose the template from the drop down, the group that was pre-assigned dissappears.  
 
      Is there any workaround on this?
 
Regards,.
Noah

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