  The $\mathcal{N}{=}\,2$ supersymmetric hyperbolic Calogero-Sutherland model
obtained in arXiv:1902.08023 by gauging the $\mathcal{N}{=}\,2$ superfield
matrix system is studied. Classical and quantum $\mathcal{N}{=}\,2$
supersymmetry generators are found. The difference in the structure of
classical and quantum supercharges is established. It is shown that, unlike
classical supercharges, quantum supersymmetry generators can be limited to an
invariant sub-sector that does not contain off-diagonal fermion operators. The
Lax pair for supersymmetric generalization of the hyperbolic
Calogero-Sutherland system is constructed.
