  The Finslerian post-Lorentzian kinematic transformations can explicitly be
obtained under uni-directional breakdown of spatial isotropy, provided that the
requirement that the relativistic unit hypersurface (indicatrix or mass shell)
be a space of constant negative curvature is still fulfilled. The method
consists in evaluating respective Finslerian tetrads and then treating them as
the bases of inertial reference frames. The Transport Synchronization has
rigorously been proven, which opens up the ways proper to favour the concept of
one-way light velocity. Transition to the Hamiltonian treatment is
straightforward, so that the Finslerian transformation laws for momenta and
frequences, as well as due Finslerian corrections to Doppler effect, become
clear. An important common feature of the ordinary pseudo-Euclidean theory of
special relativity and of the Finslerian relativistic approach under study is
that they both endeavour to establish a universal prescription for applying the
theory to systems in differing states of motion.
