  This paper is the third in a series on submillimeter galaxy magnification
bias, focusing on the tomographic scenario. It refines the methodology used to
constrain the halo occupation distribution model and cosmological parameters
within a flat $\Lambda$CDM model, using updated data. The study aims to
optimize CPU time, explore strategies for analyzing different redshift bins,
and assess the impact of excluding the GAMA15 field. The tomographic approach
involves dividing the redshift range into bins and analyzing cross-correlation
measurements between submillimeter and foreground galaxies. The results show
good agreement between the mean-redshift and full model cases, with an increase
in the minimum mass of lenses at higher redshifts. The inferred cosmological
parameters have narrower posterior distributions, indicating reduced
measurement uncertainties compared to previous studies. Excluding the GAMA15
field reduces the cross-correlation signal, suggesting sample variance within
the large-scale structure. Extending the redshift range improves robustness
against sample variance and produces similar but tighter constraints. The study
highlights the importance of sample variance and redshift binning in
tomographic analyses, and suggests using additional wide-area fields and
updated foreground catalogues for more effective implementation.
