  We calculate the $\eta^\prime$-meson energy spectrum in the decay $\Upsilon
(1S) \to \eta^\prime g g g \to \eta^\prime X$ in the leading-order perturbative
QCD in the static quark limit for the Orthoquarkonium. Our principal result is
the extraction of parameters of the $\eta^\prime g^* g$ effective vertex
function (EVF) involving a virtual and a real gluon from the available data on
the hard part of the $\eta^\prime$-meson energy spectrum. The perturbative QCD
based framework provides a good description of the available CLEO data,
allowing to constrain the lowest Gegenbauer coefficients $B^{(q)}_2$ and
$B^{(g)}_2$ of the quark-antiquark and gluonic distribution amplitudes of the
$\eta^\prime$-meson. The resulting constraints are combined with the existing
ones on these coefficients from an analysis of the $\eta-\gamma$ and
$\eta^\prime-\gamma$ transition form factors and the requirement of positivity
of the EVF, yielding $B^{(q)}_2(\mu_0^2) = -0.008 \pm 0.054$ and
$B^{(g)}_2(\mu_0^2) = 4.6 \pm 2.5$ for $\mu_0^2 = 2$ GeV$^2$. This reduces
significantly the current uncertainty on these coefficients. The resulting EFV
$F_{\eta^\prime g^* g} (p^2, 0, m_{\eta^\prime}^2)$, including the
$\eta^\prime$-meson mass effects, is presented.
