High-pressure high-temperature (HPHT) crystalline monosulfide solid solution (Mss) phases (FexNi1−xS, x = 0.90, 0.75, 0.50, 0.25), troilite (FeS I), and α-NiS of the Fe-Ni-S system were synthesized at 7 GPa and 900–1550 °C. The structural parameters of the obtained phases were refined by XRD using the Rietveld method. Factor group analysis revealed the number of active Raman modes for FeS I and α-NiS. Raman spectra of troilite, α-NiS, and Mss phases were obtained. It was shown that the Raman spectra of Mss phases and α-NiS have a similar topology. The Raman spectra of the experimental phases in the Fe-Ni-S system were analyzed with non-negative matrix factorization, which provided a meaningful concentration dependence of the spectral patterns. The spectral components were assigned to the FeS I and α-NiS structures. The structural and spectroscopic studies show linear dependencies of unit cell parameters and spectral components on composition and confirm the existence of a series of monosulfide solid solution FexNi1−xS.