if $\displaystyle B(x)$ is a scalar field in (3d space) with fourier transform $\displaystyle \widetilde{B}(p)$ and $\displaystyle x\rightarrow x'$ is a finite isometry (i.e a rotation and translation $\displaystyle x'=Rx-a$ what is the fourier transform of $\displaystyle B(x')$

I keep wanting to write $\displaystyle \widetilde{B'}(p)=e^{ip.x`}\widetilde{B}(p)$ (i.e, a change of phase) but I aint so sure and I'm too dumb to prove it. Maybe I should say that doing this works for what I intend it for.