Evolution of the spin parameter a_⋆ (the color bar) as a function of the orbital period and mass of He-rich stars with TS included at solar metallicity. The colored lines linking the two symbols show the evolution of the binary. The color along the line represents BH spins a_⋆ along the evolution from the ZAHeMS to the central carbon depletion, assuming that the He-rich star progenitors directly collapse to form BHs with mass and AM conserved.