A single crystalline layered semiconductor In1.2Ga0.8S3 phase was grown, and by intercalating p-aminopyridine (NH2-C5H4N or p-AP) molecules into this crystal, a new intercalation compound, In1.2Ga0.8S3·0.5(NH2-C5H4N), was synthesized. Further, by substituting p-AP molecules with p-ethylenediamine (NH2-CH2-CH2-NH2 or p-EDA) in this intercalation compound, another new intercalated compound—In1.2Ga0.8S3·0.5(NH2-CH2-CH2-NH2) was synthesized. It was found that the single crystallinity of the initial In1.2Ga0.8S3 samples was retained after their intercalation despite a strong deterioration in quality. The thermal peculiarities of both the intercalation and deintercalation of the title crystal were determined. Furthermore, the unit cell parameters of the intercalation compounds were determined from X-ray diffraction data (XRD). It was found that increasing the c parameter corresponded to the dimension of the intercalated molecule. In addition to the intercalation phases’ experimental characterization, the lattice dynamical properties and the electronic and bonding features of the stoichiometric GaInS3 were calculated using the Density Functional Theory within the Generalized Gradient Approximations (DFT-GGA). Nine Raman-active modes were observed and identified for this compound. The electronic gap was found to be an indirect one and the topological analysis of the electron density revealed that the interlayer bonding is rather weak, thus enabling the intercalation of organic molecules.