We derive explicit analytic results for the dynamic, nonlocal and inhomogeneous screening functions of a finite superlattice array of N equally spaced 2D quantum well plasmas embedded in infinite and semi-infinite host bulk-plasma-like media. The closed-form results presented here for the screening functions, which are space-time matrix inverses of the spatially inhomogeneous dielectric functions, are valid for any number of wells, and can accomodate nonlocality in both the 2D and host plasmas, as well as an ambient normal magnetic field.