  The exact values of the presently determined components 26of the angular Fock
coefficients at the two-particle coalescences were obtained and systematized.
The Green Function approach was successfully applied to simplify the most
complicated calculations. The boundary conditions for the Fock coefficient
components in the hyperspherical angular coordinates, which follows from the
Kato cusp conditions for the two-electron wave function in the natural
interparticle coordinates, were derived. The validity of the obtained boundary
conditions was verified on examples of all the presently determined components.
The additional boundary conditions are not arising from the Kato cusp
conditions were obtained as well. The Wolfram Mathematica was used intensively.
