  Abrikosov vortex contains magnetic field and circulating currents that decay
at a short range $\lambda \sim 100$ nm. However, the vortex can induce a long
range Josephson phase shift at distances $r\sim\mu$m$\gg\lambda$. The mechanism
of this puzzling phenomenon is not clearly understood. Here we present a
systematic study of vortex-induced phase shift in planar Josephson junctions.
We make two key observations: (i) The cutoff effect: although vortex-induce
phase shift is a long-range phenomenon, it is terminated by the junction and
does not persists beyond it. (ii) A crossover from linear to superlinear
dependence of the phase shift on the vortex polar angle occurs upon approaching
of the vortex to the junction. The crossover occurs at a distance comparable
with the penetration depth. This, together with theoretical and numerical
analysis of the problem, allows unambiguous identification of two distinct and
independent mechanisms. The short range mechanism is due to circulating vortex
currents {\it inside} superconducting electrodes without involvement of
magnetic field. The long range mechanism is due to stray magnetic fields {\it
outside} electrodes without circulating vortex currents. We argue that
understanding of controlling parameters of vortex-induced Josephson phase shift
can be used for development of compact and fast electronic devices with low
dissipation power.
