For ICRH scenarii where the majority cyclotron resonance intersects the plasma core, mode conversion of the fast magnetosonic wave to an Alfvén wave takes place at the plasma boundary on the high field side. Simple analytical estimates of the converted power for this mode conversion process are derived and compared with numerical calculations including finite electron inertia and kinetic effects. The converted power is found to depend on the local value of the wave field as well as on plasma parameters at the Alfvén wave resonance. The interference with the reflected wave will therefore modify the mode conversion. If the conversion layer is localized near the wall, the conversion will be strongly reduced. The conversion coefficient is found to be strongest for small density gradients and high density and it is sensitive to the value of the parallel wave number. Whether it increases or decreases with the latter depends on the ion composition. Analysis of this problem for ICRH in JET predicts that a large fraction of the power is mode converted at the plasma boundary for first harmonic heating of tritium in a deuterium-tritium plasma.