The Sun's contribution to climate variations was highly questioned recently. In this paper we show that bi-decadal variability of solar magnetic field, modulating the intensity of galactic cosmic ray (GCR) at the outer boundary of heliosphere, could be easily tracked down to the Earth's surface. The mediator of this influence is the lower stratospheric ozone, while the mechanism of signal translation consists of: (i) GCR impact on the lower stratospheric ozone balance; (ii) modulation of temperature and humidity near the tropopause by the ozone variations; (iii) increase or decrease of the greenhouse effect, depending on the sign of the humidity changes. The efficiency of such a mechanism depends critically on the level of maximum secondary ionisation created by GCR (i.e. the Pfotzer maximum) – determined in turn by heterogeneous Earth's magnetic field. Thus, the positioning of the Pfotzer max in the driest lowermost stratosphere favours autocatalytic ozone production in the extra-tropical Northern Hemisphere (NH), while in the SH– no suitable conditions for activation of this mechanism exist. Consequently, the geomagnetic modulation of precipitating energetic particles – heterogeneously distributed over the globe – is imprinted on the relation between ozone and humidity in the lower stratosphere (LS). The applied test for causality reveals that during the examined period 1957–2012 there are two main centres of action in the winter NH, with tight and almost stationary winter ozone control on the near tropopause humidity. Being indirectly influenced by the solar protons, the variability of the SH lower stratospheric ozone, however, is much weaker. As a consequence, the causality test detects that the ozone dominates in the interplay with ULTS humidity only in the summer extra-tropics.