B[e] supergiants (SGs) are massive post-main-sequence stars, surrounded by a complex circumstellar (CS) environment. The aim of this work is to investigate the structure and kinematics of the CS disc of the B[e] SG LHA 120-S 35. We used high-resolution optical spectra obtained in different years to model the forbidden emission lines and determine the kinematical properties of their line-forming regions, assuming Keplerian rotation. We also used low-resolution near-infrared (IR) spectra to explore the variability of molecular emission. LHA 120-S 35 displays spectral variability in both optical and IR regions. The P-Cygni line profiles of H I, as well as those of Fe II and O I, suggest the presence of a strong bipolar clumped wind. We distinguish density enhancements in the P-Cygni absorption component of the first Balmer lines, which show variations in both velocity and strength. The P-Cygni profile emission component is double-peaked, indicating the presence of a rotating CS disc. We also observe line-profile variations in the permitted and forbidden features of Fe II and O I. In the IR, we detect variations in the intensity of the H I emission lines as well as in the emission of the CO band-heads. Moreover, we find that the profiles of each [Ca II] and [O I] emission lines contain contributions from spatially different (complete or partial) rings. Globally, we find evidence of detached multi-ring structures, revealing density variations along the disc. We suggest that LHA 120-S 35 has passed through the red-supergiant (RSG) phase and evolves back bluewards in the Hertzsprung-Russell diagram. The formation of the complex CS structure could be the result of the wind-wind interactions of the post-RSG wind with the previously ejected material from the RSG. However, the presence of a binary companion can not be excluded. Finally, we find that LHA 120-S 35 belongs to a young stellar cluster.
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