Mass-transfer rate and the envelope mass as a function of time in binary models evolving through a case B mass-transfer. Different panels correspond to different initial masses of the donor (M₁). Colors indicate different metallicities. All the models were computed with initial orbital period P ≈ 225 days and initial mass ratio q = 0.6. At Solar metallicity, the case B mass transfer is always a short-lived phase (< 10⁴ yr) that strips the (nearly) entire hydrogen envelope leaving behind a stripped helium core. At subsolar metallicities of the LMC and SMC, above a certain donor mass a significant part of the envelope may be stripped on a much longer nuclear timescale of core He burning. Such donors remain only partially stripped for the duration of core-He burning.