The radio emission anomaly coincident with the 2016 glitch of the Vela pulsar may be caused by a star quake that launches Alfvén waves into the magnetosphere, disturbing the original radio emitting region. To quantify the lifetime of the Alfvén waves, we investigate a possible energy loss mechanism, the conversion of Alfvénwaves into fast magnetosonic waves. Using axisymmetric force-free simulations, we follow the propagation of Alfvén waves launched from the stellar surface with small amplitude into the closed zone of a force-free dipolar pulsar magnetosphere. We observe mode conversion happening in the ideal force-free regime. The conversion efficiency during the first passage of the Alfvén wave through the equator can be large, for waves that reach large amplitudes as they travel away from the star, or propagate on the field lines passing close to the Y-point. However, the conversion efficiency is reduced due to dephasing on subsequent passages and considerable Alfvén power on the closed field lines remains. Thus while some leakage into the fast mode happens, we need detailed understanding of the original quenching in order to say whether mode conversion alone can lead to reactivation of the pulsar on a short timescale.