quantum mechanics - Aharonov-Bohm phase picked up when a magnetic dipole goes around a charge

When a particle with charge $q$ traverses a loop that encloses a magnetic flux $\Phi$, it picks up a phase $e^{iq\Phi}$ (I have set $c$ and $\hbar=1$). This is the usual Aharonov-Bohm phase. Now, let us look at a different scenario - consider a particle with a magnetic dipole moment that gives rise to a flux $\Phi$ through a plane. Move this particle along a loop enclosing a charge $q$ in the same plane. What is the phase picked up in this case?

According to Section 2.1.3 of Intro. to Topological Quantum Computation by Pachos, this phase is also $e^{iq\Phi}$. I am not able to see why, though.