<p>The light plagioclase-enriched crust as well as the KREEP layer at the surface of the Moon are believed to be remnants of the bottom-up crystallization of a global Lunar Magma Ocean. &#160;In such a setup, the primitive Lunar solid mantle is coated by a liquid magma ocean of similar composition. We propose here to study the dynamic and evolution of the primitive Lunar solid mantle, accounting for the presence of the Lunar Magma Ocean.</p><p>We solve numerically the equations of solid-state convection in the solid part of the mantle. &#160;This model is coupled to 1D models of crystallization of the magma oceans to self-consistently compute the thickening of the solid part as heat is evacuated from the mantle. &#160;We take into account fractional crystallization at the freezing front.</p><p>Moreover, the boundaries between the solid and the magma oceans are phase-change interfaces. &#160;Convecting matter in the solid arriving near the boundary or getting away from it forms a topography which can be erased by melting or freezing. &#160;Hence, provided the melting and freezing occurs rapidly compared to the time needed to build the topographies by viscous forces, dynamical exchange of matter can occur between the solid mantle and the magma oceans. &#160;We take this effect into account in our model with a boundary condition applied to the solid.</p><p>We find that the boundary condition allowing matter to cross the interfaces between the solid and the magma oceans greatly affects the convection patterns in the solid as well as its heat flux. &#160;Larger-scale convection patterns are selected compared to the classical case with non-penetrative boundary conditions; and the heat transfert in the solid is more efficient with these boundary conditions. &#160;This affects the long term thermal evolution of the mantle as well as the shape of chemical heterogeneities that can be built by fractional crystallization of magma oceans.</p>