Have you opened the script?
storeGameObject.Value = Owner;
It seems that Owner is a property defined in FsmStateAction class, thus you can access it from every class that inherits from FsmStateAction.
But, you can set the FSM in the prefab itself and store the owner with no problem with Playmaker. However, if you want to identify instances of a prefab, you are to need quite a lot of different globals, if you were to instantiate many copies of your prefab.
What I'd do is something like get the gameObject property? If you have a script attached to any gameObject and you want to get THAT gameObject from it's own component...
FsmGameObject ownerGO;
ownerGO.Value = this.gameObject;
If you are accessing it from a custom action, just calling the Owner property might do. Guess FsmStateAction class manages it somehow. And, if you're attempting to send an event (perhaps via script, as well?), you should think as well on sending the event to the Fsm or PlayMakerFSM component of that gameObject.
I don't think I'm getting your problem, but I hope this helps you somehow.