  Cavity magnomechanics provides a readily-controllable hybrid system, that
consisted of cavity mode, magnon mode, and phonon mode, for quantum state
manipulation. To implement a fast-and-robust state transfer between the hybrid
photon-magnon mode and the phonon mode, we propose two accelerated
adiabatic-passage protocols individually based on the counterdiabatic
Hamiltonian for transitionless quantum driving and the Levis-Riesenfeld
invariant for inverse engineering. Both the counterdiabatic Hamiltonian and the
Levis-Riesenfeld invariant generally apply to the continuous-variable systems
with arbitrary target states. It is interesting to find that our
counterdiabatic Hamiltonian can be constructed in terms of the creation and
annihilation operators rather than the system-eigenstates and their
time-derivatives. Our protocol can be optimized with respect to the stability
against the systematic errors of coupling strength and frequency detuning. It
contributes to a quantum memory for photonic and magnonic quantum information.
We also discuss the effects from dissipation and the counter-rotating
interactions.
