Deep Space cannons: how many times can they shoot?
I'm not claiming an authoritative answer, but when playing recently the rule we followed is the activation rule -- the adjacent PDS may fire into a system that has been activated. So, in your scenario, the PDS would fire only one time.

From the TI3 Rule book (page 29):


  When a player activates a system in range of an
  enemy PDS unit, the owners of any enemy PDS units
  in range may, after the movement step of the
  Activation Sequence, fire once per PDS at any units
  in the system owned by the activating player. Note
  that when firing your PDS units during another player's
  activation, you may only fire at the units controlled 
  by the activating player. It is thus not possible
  to draw third party PDS fire at an enemy fleet by simply 
  activating its system from afar.


Although I haven't sussed this out with my gaming group, I imagine a transfer action would invoke two opportunities for an adjacent PDS if the system holding the PDS is adjacent to both transfer-action-activated systems.