Binary evolution model for J0658 assuming a CO–white-dwarf companion. Left: Hertzsprung–Russell track of the helium star (solid line) and simultaneous change of the orbital period (dash-dotted line) as well as the current position of J0658 (orange diamond). Right: Mass-transfer history after the onset of Roche lobe overflow. Solid, dashed and dash-dotted curves denote the donor’s mass-loss rate, the WD accretion rate, and the growing WD mass, respectively. Insets list the adopted initial parameters and the final values reached at the end of the computation.