Richard P. answered 06/04/20
PhD in Physics with 10+ years tutoring experience in STEM subjects
Gauss’ law says that the electric field for R1 < r < R2 = (1/4 pi epsilon0) (q + Qinner) /r^2
where Qinner is the charge on the inner surface of the shell. However, the electric field inside a conductor must be zero. Hence Qinner = -q
From there is easy to see that the contribution to the electric field due to Qinner is
-(1/ 4pi epsilon0) q / r^2.
The charge on the outer surface of the shell is Q + q and contributes nothing to the electric field
for R1 < r < R2