In electrostatic conditions does it make sense to have a dielectric material with a non-zero induced surface density of charge at one surface and no induced surface charge density at the opposite surface? This is the result I've found for a dielectric sphere surrounding a conducting sphere with a net charge Q, but I'm not sure it is correct. The result I obtained is that at the inner surface the charge density is just the one corresponding to the conducting sphere and at the outter surface the charge density is zero, does this make sense? Obviously this could not happen if it were a conducting material instead of a dielectric. Is this result due to the polarization inside the material?
When you apply an electric field to an interface of dielectrics with different conductivities, in general, a free areal interface charge will accumulate so that the normal current continuity condition will be satisfied. See Surface charge density in conducting plate and Free charge in a dielectric .
Regarding your spheres. If I understand correctly, the inner conducting sphere has a surface charge and the outer not conducting dielectric sphere has no free surface charge. This is correct and corresponds to the continuity of electric displacement. As a consequence of Gauss law, you should have an electric displacement corresponding to the inner charge at the dielectric sphere surface and beyond.