I. INTRODUCTION The problem of magnetoresistance in the hoping transport was addressed decades ago. In particular, an interest to this topic was related to important additional information provided by corresponding experiments (including estimates of the localization length). The most general and natural mechanism of positive magnetoresistance of orbital nature is related to shrinkage of the localized wave function by magnetic field; it was extensively reviewed in [1]. Then another important mechanism of orbital magnetoresistance was considered by Nguen, Shklovskii and Spivak (for the review see [2]). It is related to a presence of under-barrier scattering of hopping electrons by intermediate hopping sites and to interference between dif- ferent hopping trajectories. Note that for the effective interference the difference of lengths of different trajectories should not exceed the localization length which restrict the location of the trajectories to so-called ”cigar region”. A significance of this mechanism was empha- sized by the factor of exponentially-broad scatter of hopping probabilities corresponding to different ”hopping resistors”. As a result of ”logarithmic averaging” over different config- urations the most important role is played by those interference patterns where the total hopping probability almost vanishes as a result of the destructive interference. The magnetic field suppresses the interference and thus the average effect is negative magnetoresistance which appears to be linear at weak magnetic field (although becoming quadratic at H → 0). An important features of the approach discussed in [2] were as follows. First, the authors exploited an assumption of a presence of many intermediate scatterers. Second, following the theory [3], the authors assumed the preexponential factor to be equal to µ/r where µ is scattering amplitude, r is a distance between the hopping site and the scattering center. The picture of interference magnetoresistance considered in [2] was very rich including a change of the sign of magnetoresistance, effects of spin glass etc. Somewhat later the problem was also discussed in [4], [5] where it was noticed that in realistic situations the number of intermediate scatterers is small and most probably equal to one or (in average) even less. Another important ingredient of the paper [5] was a usage of wave functions typical for Coulomb centers which have not contained preexponential depending on r . In contrast to the ”scattering states” of [2] which contained preexponential factors decaying with r , this situation can be specified as ”strong scattering case”. Note that, although in [5] the authors considered 2D hopping, they addressed to the case of 2