In this study, we investigate magnetic properties of umbra of magneto-conjugate leading and following sunspots, i.e. connected through magnetic field lines. We established dependences between individual sunspot umbra field characteristics, and between these characteristics on the umbra area ($S$) separately for sunspot pairs, for which the minimal angle between the umbra magnetic field line of the leading ($L$) sunspot and the positive normal line to the Sun surface is smaller, than that in the following ($F$) sunspot ($alpha_{min-L}<alpha_{min-F}$; such sunspot pairs are the bulk) and, on the contrary, when $alpha_{min-L}>alpha_{min-F}$. The $alpha_{min-L}(S_L)$, $alpha_{min-F}(S_F)$, $B_{max-L}(S_L)$ and $B_{max-F}(S_F)$ dependences are shown to have similar behavior features, and are quantitatively close for two sunspot groups with a different asymmetry of the sunspot magnetic field connecting them (here, $B_{max-L,F}(S_L)$ is the magnetic induction maximum induction in umbrae of the leading and the following sunspots). The dependence of mean values of angles within umbra $<alpha_{L,F}>$ on the sunspot umbra area $S_{L,F}$ and on the mean value of magnetic induction in umbra $<B_{L,F}>$ appeared different for two cases. Also, in the bulk of the investigated sunspot pairs, the leading sunspot was shown to appear closer to the polarity inversion line between the sunspots, than the following one. This result and the conclusion that, in the bulk of the investigated pairs of the magnetically conjugate sunspots, $alpha_{min-L}<alpha_{min-F}$ are closely coupled.
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