  The experimental studies of the paramagnetic-antiferromagnetic phase
transition through M\"{o}ssbauer spectroscopy and measurements of temperature
and field dependencies of magnetic susceptibility in the layered
Cu$_{0.15}$Fe$_{0.85}$PS$_3$ crystal are presented. The peculiar behavior of
the magnetization - field dependence at low-temperature region gives evidence
of a weak ferromagnetism in the studied alloy. By the ab initio simulation of
electronic and spin subsystems, in the framework of electron density functional
theory, the peculiarities of spin ordering at low temperature as well as
changes in interatomic interactions in the vicinity of the Cu substitutional
atoms are analyzed. The calculated components of the electric field gradient
tensor and asymmetry parameter for Fe ions are close to the ones found from
M\"{o}ssbauer spectra values. The Mulliken populations show that the main
contribution to the ferromagnetic spin density is originated from $3d$-copper
and $3p$-sulfur orbitals. The estimated total magnetic moment of the unit cell
(8.543~emu/mol) is in reasonable agreement with the measured experimental value
of $\sim9$~emu/mol.
