Why?! In what way, in what possible way, could taking Ichigo's fullbring give Ginjou access to ICHIGO'S own inner spirit/hollow?! That's like saying because he stole Ichigo's ability, that he gets his own Zangetsu to talk to, too. And I think we can all agree on how silly that sounds.
Ginjou has Ichigo's rietsu, and can copy his abilities; he does NOT have the inner spirits that drive those powers, because they are unique to Ichigo. So stop saying that--It makes Kubo sound like a really terrible author, and he really isn't THAT bad.