Discrete { PT} -symmetric models of scattering

One-dimensional scattering mediated by non-Hermitian Hamiltonians is studied. A schematic set of models is used which simulates two point interactions at a variable strength and distance. The feasibility of the exact construction of the amplitudes is achieved via the discretization of the coordinate. By direct construction it is shown that in all our models the probability is conserved. This feature is tentatively attributed to the space- and time-reflection symmetry (also known as -symmetry) of our specific Hamiltonians.