  The existence of decompositions of the form $f=P\cdot q+r$ with
$P_k^{\ast}\left( D\right) r=0 $, where $f$ is entire, $P$ a polynomial and
$P^{\ast}_k$ the principal part of $P$ with its coefficients conjugated, was
achieved in \cite{AlRe23} under certain restrictions on the order of $f$. Here
we prove uniqueness, thereby obtaining Fischer decompositions, under conditions
that sometimes match those required for existence, and sometimes are more
restrictive, depending on the parameters involved.
