When I use the search facility in Projects and the results include tasks, it is not possible to manage the task from that view.  It is also not possible to get the the task list that the task resides in - all you can do is open the task which then gives access to the task list.  To manage the task (such as moving it to another list) you have to follow the link to the list uit currently resides in and then manually search for the same task again to move it.

 

 

thanks