Ginjo absorbed, Ichigo's Fullbrings powers, powers comes from reiatsu (better to say reiryoku), therefore he absorbed Ichigo's reiryoku. Translation for Reiryoku is spiritual powers.Ginjo absorbed Ichigos shinigami powers. IE the powers of his zan. If it was a shiba ability, then why can Ginjo use it. Also ichigo in fullbring was using a mock GT, similar, but it can't be s legitimate one.
He can use GT because he absorbed Ichigo's reiryoku and Ichigo is from Shiba clan.
I don't see how Ichigo's GT in FB is mock GT. It is legitimate just as his GT in shinigami form.