  Magnification bias, an observational effect of gravitational lensing in the
weak regime, allows testing the cosmological model through angular correlations
of sources at different redshifts. This effect has been observed in various
contexts, particularly with sub-millimeter galaxies (SMGs), offering
astrophysical and cosmological insights. The study aims to investigate the
magnification bias effect exerted by galaxy clusters on SMGs and its
implications for astrophysical and cosmological parameters within the
$\Lambda$CDM model. Magnification bias was explored through quantifying the
cross-correlation function, utilised to derive constraints on cosmological and
astrophysical parameters with a Markov Chain Monte Carlo algorithm. Two
distinct galaxy cluster samples were used to assess result robustness and
understand the influence of sample characteristics. Cluster samples show higher
cross-correlation values than galaxies, with an excess at larger scales
suggesting contributions from additional large-scale structures. The parameters
obtained, while consistent with galaxies, are less constrained due to broader
redshift distributions and limited cluster statistics. Results align with weak
lensing studies, hinting at slightly lower $\sigma_8$ and $\Omega_m$ values
than \emph{Planck}'s CMB data, emphasizing the need for enhanced precision and
alternative low-redshift universe tests. While yielding constraints compatible
with the $\Lambda$CDM model, limitations include broader redshift distributions
and a limited number of lenses, resulting in less constrained parameters
compared to previous galaxy studies. Nonetheless, the study underscores the
potential of using galaxy clusters as lenses for magnification bias studies,
capitalising on their elevated mass, providing a promising avenue to test
current Cosmology theories. Further progress can be made by expanding the lens
sample size.
