In order to predict the spins of stellar remnants we need to understand the evolution of the internal rotation of stars, and to identify at which stage the rotation of the contracting cores of evolved stars decouples from their expanding envelopes. The donor stars of mass transferring binaries lose almost their entire envelope and may thus offer a direct view on their core rotation. After the mass transfer event they contract and fade rapidly, although they are well observable when caught in the short-lived B-star phase. The B-type primary of the galactic binary system LB-1, which was originally suggested to contain a massive black hole, is nicely explained as a stripped star accompanied by a fainter Be star. The narrow absorption lines in the primary’s spectrum signify extremely slow rotation, atypical of B-type main-sequence stars. Here we investigate the evolution of mass donors in generic grids of detailed binary evolution models, where both stars include differential rotation, internal angular momentum transport, and spin-orbit coupling. Whereas the mass gainers are typically spun-up during the mass transfer, we find that the spins of the stripped donor models depend sensitively on the employed mechanism for internal angular momentum transport. Purely hydrodynamic transport cannot explain the observed slow rotation, while models including magnetic angular momentum transport are able to reproduce the observed rotation of LB-1 and similar stars, independent of the initial rotation rate. In such models the spin of the white dwarfs that emerge at the end of the evolution is independent of the mass stripping. We find evidence that the mass transfer in LB-1 was moderately non-conservative.