Quantum-symmetric equivalence is a graded Morita invariant

We show that if two m-homogeneous algebras have Morita equivalent graded module categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal equivalence between the categories of comodules for their associated universal quantum groups (in the sense of Manin) which sends one algebra to the other. As a consequence, any Zhang twist of an m-homogeneous algebra is a 2-cocycle twist by some 2-cocycle from its Manin's universal quantum group.