Thank you everyone!!

@ Michael, I'm sure MoI exported the obj file correctly because Blender has no problem in seeing the different parts.

@ BurrMan, I tried with "Import Object", "Import Model for Voxelization" and "Import Model for Per Pixel Painting" (I noticed that sometimes there's one solid model in the sculpt room but the painting room preserves all the various parts).
This thing is puzzling me, it's not the first time I import a model from MoI to 3D Coat...