  Dynamical properties of an impurity spin coupled symmetrically to sublattices
of ordered 2D Heisenberg quantum antiferromagnet (i.e., frustrated impurity
spin) are discussed at $T\ge0$ (existence of a small interaction stabilizing
the long range order at $T\ne0$ is implied). We continue our study on this
subject started in Phys.Rev.B 72, 174419 (2005), where spin-1/2 defect is
discussed and the host spins fluctuations are considered within the spin-wave
approximation (SWA). In the present paper we i) go beyond SWA and ii) study
impurities with spins $S\ge1/2$. It is demonstrated that in contrast to defects
coupled to sublattices asymmetrically longitudinal host spins fluctuations play
important role in the frustrated impurity dynamics. The spectral function, that
is proportional to $\omega^2$ within SWA, acquires new terms proportional to
$\omega^2$ and $\omega T^2$. It is observed that the spin-1/2 impurity
susceptibility has the same structure as that obtained within SWA: the Lorenz
peak and the non-resonant term. The difference is that the width of the peak
becomes larger being proportional to $f^2(T/J)^3$ rather than $f^4(T/J)^3$,
where $f$ is the dimensionless coupling parameter. We show that transverse
static susceptibility acquires a new negative logarithmic contribution. In
accordance with previous works we find that host spins fluctuations lead to an
effective one-ion anisotropy on the impurity site. Then defects with $S>1/2$
appears to be split. We observe strong reduction of the value of the splitting
due to longitudinal host spins fluctuations. We demonstrate that the dynamical
impurity susceptibility contains $2S$ Lorenz peaks corresponding to transitions
between the levels, and the non-resonant term.
