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In this study, we investigate magnetic properties of umbra ofmagneto-conjugate leading and following sunspots, i.e. connected throughmagnetic field lines. We established dependences between individual sunspotumbra field characteristics, and between these characteristics on the umbraarea ($S$) separately for sunspot pairs, for which the minimal angle betweenthe umbra magnetic field line of the leading ($L$) sunspot and the positivenormal 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, andare quantitatively close for two sunspot groups with a different asymmetry ofthe sunspot magnetic field connecting them (here, $B_{max-L,F}(S_L)$ is themagnetic induction maximum induction in umbrae of the leading and the followingsunspots). 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 ofmagnetic 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 toappear closer to the polarity inversion line between the sunspots, than thefollowing one. This result and the conclusion that, in the bulk of theinvestigated pairs of the magnetically conjugate sunspots,$\alpha_{min-L}<\alpha_{min-F}$ are closely coupled.

On the nature of the magnetic field asymmetry in magnetically coupled  leading and following sunspots observed in active regions with no eruptive  events