Möbius transformation of nonconcentric circles

Question

Is there any transformation that can match two circles with equal radii (say $r_0$) which are positioned at $(0,0)$ and $(X_0, Y_0)$ to two concentric circles? I know there is a transformation when $Y_0$ is equal to zero, but I need both $X_0$ and $Y_0$ to be nonzero. The initial circles do not collide which means $X_0^2+Y_0^2>>4 r_0^2$. I should also note that I don't like to use rotation to make $Y_0$ equal to zero because my boundary condition is difficult. What is the transformation that can do the job?