Inorganic WS2 nanotubes (INT-WS2) were embedded into sub-mu m polyvinylidene fluoride-co-hexafluropropylene (PVDF-HFP) electrospun fibers. In this report we explore the Raman scattering spectroscopy from a single nanotube during stretching of individual nanocomposite fibers. Red shifts of up to similar to 4.7 cm(-1) for A(1g) and E-2g(1) WS2 bands were found before reaching the "tearing point" of the fibers. These shifts may correlate with up to similar to 2.8% of the WS2 nanotube elongation. Moreover, the absence of the A(1g) and E-2g(1) bands' broadening, as well as the nonappearance of the E-2g(2) shear mode in the nanotube Raman spectra, suggest the stretching of the nanotubes as a whole (including inner layers). These results point to the excellent adhesion of the nanotubes' surface to the polymer and to the effective load transfer from the polymer to the WS2 nanotube. In order to elucidate the nature of interaction between the polymer and the nanofiller, we modeled the deformation of composite fibers using an elastic lattice spring model (LSM). The results of the model are fully consistent with our interpretation.