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) is presented in this paper, including its design, modeling, tolerance analysis, and experimental characterizations of the angular and intensity distributions among 2 × 4 output beams and the power efficiency. A quantum cascade laser (QCL) is used to generate the input beam for evaluation of the grating performance in its all relevant aspects with an accuracy level never reported before, where good agreements with modeling results are found. This is the first asymmetric-profile grating fully modelled and characterized at a THz frequency, that further confirms the versatility of this technology for providing an intermediate optical element for feeding multiple array detectors with a single radiation source at such a scientifically interesting frequency regime.