  Using transfer-matrix extended phenomenological renormalization-group methods
the critical properties of spin-1/2 Ising model on a simple-cubic lattice with
partly anisotropic coupling strengths ${\vec J}=(J',J',J)$ are studied.
Universality of both fundamental critical exponents $y_t$ and $y_h$ is
confirmed. It is shown that the critical finite-size scaling amplitude ratios
$U=A_{\chi^{(4)}}A_\kappa/A_\chi^2$, $Y_1=A_{\kappa^{''}}/A_\chi$, and
$Y_2=A_{\kappa^{(4)}}/A_{\chi^{(4)}}$ are independent of the lattice anisotropy
parameter $\Delta=J'/J$. By this for the last above invariant of the
three-dimensional Ising universality class we give the first quantitative
estimate: $Y_2\simeq2.013$ (shape $L\times L\times\infty$, periodic boundary
conditions in both transverse directions).
