We will report a full demonstration of the Fourier phase grating used as 4.7 THz local oscillator (LO) multiplexer for Galactic/Extragalactic ULDB Spectroscopic Terahertz Observatory (GUSTO). The design, modeling, tolerance analysis, and experimental characterization of the angular and intensity distributions among 2 × 4 output beams and the power efficiency will be presented. This is the first detailed study of a THz beam multiplexer, which will be actually integrated in an observatory.@en