Alpha-induction is a tensor functor producing a new fusion category from a unitary modular tensor category and a Q-system in it. This can be formulated in terms of quantum 6j-symbols and braiding and gives alpha-induced bi-unitary connections. Last year, we showed that locality of the Q-system implies flatness of the alpha-induced connections. We now prove that the converse also holds, which was against expecation. We work out various examples.