  The problem is posed of further extending the axiomatic construction proposed
in Part 1 for non-local point transformations mapping in each other different
curved space times. The new transformations apply to curved space times when
expressed in arbitrary coordinate systems. It is shown that the solution
permits to achieve an ideal (Gedanken) experiment realizing a suitable kind of
phase-space transformation on point-particle classical dynamical systems.
Applications of the theory are discussed both for diagonal and non-diagonal
metric tensors.
