We consider the problem of reflectionless propagation of PT-symmetric
solitons described by the nonlocal nonlinear Schroedinger equation on a line in
the framework of the concept of transparent boundary conditions for evolution
equations. Transparent boundary conditions for the nonlocal nonlinear
Schroedinger equation are derived. The absence of backscattering at the
artificial boundaries is confirmed by the numerical implementation of the
transparent boundary conditions.