Illustration of the complete evolution of a typical LMC X-3 PPS from the ZAMS to a double CO (BH+WD) binary. Panel a) shows the evolution of the orbital period in days on a logarithmic scale. Panel b) displays the evolution of the masses in the binary system; the primary star M₁ as a star and as a BH (black line), and the companion star M₂ (blue line). The black star label indicates the time of BH formation. Panel c) shows the evolution of the system eccentricity e in yellow, while in red we show the BH spin parameter a_∗. Panel d) shows the effective temperature T_eff of the donor star on a logarithmic scale. Data from the BSE simulation are shown as dashed lines, while data from MESA as plotted solid lines. From Table 1 we have added in panel a) the observed orbital period as the green dotted line, in panel b) the 1σ and 2σ error of M₂ and M_BH centered on the observed values, in panel c) the red dotted line is the upper 2σ limit on the BH spin parameter, and in panel d) the 1σ and 2σ error of T_eff. In general, there is a fine agreement between BSE and MESA at the moment of RLO, except for the age of the system at RLO onset. MESA calculations find that RLO onset occurs at time =8.8 Myr, whereas BSE finds it to begin at time =12.2 Myr. The reason for the discrepancy is the differences in the micro physics, between BSE and MESA, and in particular in the stellar structure calculations. Here, for illustrating purposes, the MESA calculations are offset to the right by 2.4 Myr to generate a smooth transition in the figure. The star marks the formation of the BH at ~8 Myr and the vertical dashed line marks the time ~42 Myr at which the system crosses the observed orbital period.