The dispersion-corrected density functional theory (DFT-D) is applied for investigation of structure and electronic properties of a sulfur-terminated graphene nanoribbon (S-GNR) encapsulated in a carbon nanotube. Two mechanisms of accommodation of the GNR in the carbon nanotube, distortion of the nanotube cross-section into an elliptic shape accompanied by bending of the GNR and transformation of the GNR to a helical conformation, are analyzed. Three types of elastic distortions of the nanotube and encapsulated GNR are revealed depending on the ratio of the diameter of the nanotube cavity to the GNR width. Helical states of the GNR are shown to be stabilized by the van der Waals attraction of sulfur atoms at neighbouring edges of adjacent turns of the GNR. The results of calculations are correlated with the experimental observations for the S-GNR synthesized recently inside the carbon nanotube. The hybrid DFT calculations of band structures of zigzag GNRs terminated with different atoms demonstrate that as opposed to O- and H-GNRs, the S-GNR is metallic even when deformed inside carbon nanotubes. Possible applications of GNRs encapsulated in carbon nanotubes are discussed.