Hi Bikhu,
I hope the attached scene file contains all information you need.
Note that the shadow is based on the Color Channel, or the missing information thereof in the shadow area. If the Illumination channel by itself can’t receive shadow.
The Color channel will add color-values to the surface, but the Illumination is the only one that stays - so the Illuminations channel provides the shadow color.
There might be more, but let me know what you need, please with a little scene file.
As a side note: I have used a Diffusion-Map to “fake” the shadow in the Luminance channel. Typically in Camera Projection I use the Luminance channel only (vs Color and Luminance), in that case the light is baked already in the projected image. To get an extra shadow in that scene, just painted that shadow in. The last awarded work where I did it was in a music video, which can be found on my YouTube channel. (Video and Making of)
All the best