Opaque substrates precluded, so far, transmission studies of II-VI semiconductor microcavities. This work presents the design and molecular beam epitaxy growth of semimagnetic (Cd,Zn,Mn)Te quantum wells embedded into a (Cd,Zn,Mg)Te-based microcavity, which can be easily separated from the GaAs substrate. Our lift-off process relies on the use of a MgTe sacrificial layer which stratifies in contact with water. This allowed us to achieve a II-VI microcavity prepared for transmission measurements. We evidence the strong light-matter coupling regime using photoluminescence, reflectivity, and transmission measurements at the same spot on the sample. By comparing a series of reflectance spectra before and after lift-off, we prove that the microcavity quality remains high. Thanks to Mn content in quantum wells we show the giant Zeeman splitting of semimagnetic exciton-polaritons in our transmitting structure.