  Buan-Iyama-Reiten-Smith proved, based on Derksen-Weyman-Zelevinsky work, that
the Jacobian algebra of two quivers with potential related by a QP-mutation are
nearly Morita equivalent. They proved, using Axiom of Choice, that the natural
functor $\mu_k$ is an equivalence by showing that $\mu_k$ is full, faithfull
and dense. In this note we provide a quasi-inverse $\mu_k^-$ to $\mu_k$ without
Axiom of Choice.
