Context. The intriguing binary LS V +22 25 (LB-1) has drawn much attention following claims of it being a single-lined spectroscopic binary with a 79-day orbit comprising a B-type star and a ≈70 M_⊙ black hole – the most massive stellar black hole reported to date. Subsequent studies demonstrated a lack of evidence for a companion of such great mass. Recent analyses have implied that the primary star is a stripped He-rich star with peculiar sub-solar abundances of heavy elements, such as Mg and Fe. However, the nature of the secondary, which was proposed to be a black hole, a neutron star, or a main sequence star, remains unknown. Aims. Based on 26 newly acquired spectroscopic observations secured with the HERMES and FEROS spectrographs covering the orbit of the system, we perform an orbital analysis and spectral disentangling of LB-1 to elucidate the nature of the system. Methods. To derive the radial velocity semi-amplitude K₂ of the secondary and extract the spectra of the two components, we used two independent disentangling methods: the shift-and-add technique and Fourier disentangling with FDBinary. We used atmosphere models to constrain the surface properties and abundances. Results. Our disentangling and spectral analysis shows that LB-1 contains two components of comparable brightness in the optical. The narrow-lined primary, which we estimate to contribute ≈55% in the optical, has spectral properties that suggest that it is a stripped star: it has a small spectroscopic mass (≈1 M_⊙) for a B-type star and it is He- and N-rich. Unlike previous reports, the abundances of heavy elements are found to be solar. The “hidden” secondary, which contributes about 45% of the optical flux, is a rapidly rotating (vsini ≈ 300 km s⁻¹) B3 V star with a decretion disk – a Be star. As a result of its rapid rotation and dilution, the photospheric absorption lines of the secondary are not readily apparent in the individual observations. We measure a semi-amplitude for this star of K₂ = 11.2 ± 1.0 km s⁻¹ and adopting a mass of M₂ = 7 ± 2 M_⊙ typical for B3 V stars, we derive an orbital mass for the stripped primary of M₁ = 1.5 ± 0.4 M_⊙. The orbital inclination of 39 ± 4° implies a near-critical rotation for the Be secondary (v_eq ≈ 470 km s⁻¹). Conclusions. LB-1 does not contain a compact object. Instead, it is a rare Be binary system consisting of a stripped star (the former mass donor) and a Be star rotating at near its critical velocity (the former mass accretor). This system is a clear example that binary interactions play a decisive role in the production of rapid stellar rotators and Be stars.