This paper studies the boundary output feedback stabilization of reaction-diffusion PDEs in the presence of an arbitrarily long distributed input delay. The boundary control applies at the right boundary through a Robin boundary condition while the system output is selected as the left boundary Dirichlet trace. The actual control input applies to the boundary via a distributed delay spanning over a finite time interval. The proposed control strategy leverages a predictor feedback relying on Artstein's reduction method and is coupled with a finite-dimensional observer. Provided a structural controllability assumption, sufficient stability condition are derived and are shown to be always feasible provided the order of the observer is selected to be large enough.