Converting RGB to Grayscale by reference

There is such a problem.

There is shooting on a color camera with a ColorChecker. And there is shooting on another, grayscale camera with the same color checker. Is it possible to somehow convert the first RGB image to the second (Grayscale) based on the ColorChecker?
I found a tutorial on how to do this in 3D Lut Creator, but it seems that the result is not completely accurate there.
How else can you do this?