This article proves the well posedness of the boundary value problem that arises when PML algorithms are applied to Pauli's equations with a three dimensional rectangle as computational domain. The absorptions are positive near the boundary and zero far from the boundary so are always x-dependent. At the flat parts of the boundary of the rectangle, the natural absorbing boundary conditions are imposed. The difficulty addressed is the analysis of the resulting variable coeffi- cient problem on the rectanglar solid with its edges and corners. The Laplace transform is analysed. It turns on the analysis of a boundary value problem formally obtained by complex stretching. Existence is proved by deriving a boundary value problems for a complex stretched Helmholtz equation on smoothed domains. This is the first stability proof with x-dependent absorptions on a bounded domain whose boundary is not smooth.