  Quantum conversion or interface is one of the most prominent protocols in
quantum information processing and quantum state engineering. We propose a
photon-phonon conversion protocol in a hybrid magnomechanical system comprising
a microwave optical mode, a driven magnon mode and a mechanical-vibrating mode.
The microwave photons in the optical cavity are coupled to the magnons by the
magnetic-dipole interaction, and the latter are coupled to the mechanical
phonons by the magnetostrictive interaction. With strong photon-magnon
interaction and strong driving on magnon, an effective Hamiltonian is
constructed to describe the conversion between photons and phonons nearby their
resonant point. The cavity-magnon system can then play the role of a quantum
memory. Moreover, the faithfulness of the photon-phonon conversion is estimated
in terms of fidelities for state evolution and state-independent transfer. The
former is discussed in the Lindblad master equation taking account the leakages
of photon, phonon and magnon into consideration. The latter is derived by the
Heisenberg-Langevin equation considering the non-Markovian noise from the
structured environments for both optical and mechanical modes. The
state-evolution fidelity is found to be robust to the weak leakage. The
transfer fidelity can be maintained by the Ohmic and sub-Ohmic environments of
the photons and is insensitive to the $1/f$ noise of the phonons. Our work thus
provides an interesting application for the magnon system as a photon-phonon
converter in the microwave regime.
