In this technical note, we develop a full state feedback law for disturbance rejection in systems described by linear 2 x 2 partial differential equations of the hyperbolic type, with the disturbance modelled as an autonomous, finite dimensional linear system affecting the PDE's left boundary, and actuation limited to the right boundary. The effect of the disturbance is rejected at an arbitrary point in the domain within a finite time. The performance is demonstrated through simulation.