What is the equivalent of the delay theorem when dealing with Spherical Harmonics ?

Let's define:

c_f(l,m) = \int_0^\pi \int_0^{2\pi} f(\theta,\phi) Y_l^m(\theta,\phi) \sin(\theta) d\theta d\phi

I apply a rotation R= that changes (\theta,\phi) \rightarrow (\theta_R,\phi_R) and I define g(\theta,\phi) = f(\theta_R,\phi_R)

Is there a way to get:

c_g(l,m) = \gamma(\theta,\theta_R,\phi,\phi_R) c_f(l,m)

I have read about the addition theorem:

P_l(cos(\Theta)) = \sum_{m=-l}^l Y_l^m(\theta,\phi)^{*} Y_l^m(\theta_R,\phi_R)

with \Theta the angle between (\theta,\phi) and  (\theta_R,\phi_R)

I guess it is related but i don't know how...

Can anyone help me ?