  Weak gravitational lensing simulations serve as indispensable tools for
obtaining precise cosmological constraints. In particular, it is crucial to
address the systematic uncertainties in theoretical predictions, given the
rapid increase in galaxy numbers and the reduction in observational noise. Both
on-the-fly and post-processing methods for constructing lensing light-cones
encounter limitations due to the finite simulated volume, necessitating the
replication of the simulation box to encompass the volume to high redshifts. To
address this issue, our primary focus lies on investigating and quantifying the
impact of box replication on the convergence power spectrum and higher-order
moments of lensing fields. By combining the KS test with these statistics, we
confirm that there is a probability exceeding 99\% to observe the significant
statistical deviation from the correct measurements for all investigated
special line-of-sight directions, e.g., x-axis direction. Additionally, we have
developed a code that facilitates the identification of optimal viewing angles
for the light-cone construction. This code has been made publicly accessible.
