Summary: This paper studies the inhomogeneous defocusing coupled Schrödinger system \[ i \dot{u}_j + \Delta u_j = |x|^{-\rho} \bigg(\sum_{1 \leq k \leq m} a_{jk} |u_k|^p \bigg) |u_j|^{p-2} u_j, \quad \rho>0, \, j \in [1, m]. \] The goal of this work is to prove the scattering of energy global solutions in the conformal space made up of \(f \in H^1 (\mathbb{R}^N)\) such that \(xf \in L^2 (\mathbb{R}^N)\). The present paper is a complement of the previous work by the first author and Ghanmi [T. Saanouni and R. Ghanmi, Inhomogeneous coupled non-linear Schrödinger systems, J. Math. Phys. 62 (2021), no. 10, Paper No. 101508]. Indeed, the supplementary assumption \(x u_0 \in L^2\) enables us to get the scattering in the mass-sub-critical regime \(p_0 < p \leq \frac{2-\rho}{N} + 1\), where \(p_0\) is the Strauss exponent. The proof is based on the decay of global solutions coupled with some non-linear estimates of the source term in Strichartz norms and some standard conformal transformations. Precisely, one gets \[ |t|^{\alpha} \|u(t)\|_{L^r (\mathbb{R}^N)} \lesssim 1 \] for some \(\alpha>0\) and a range of Lebesgue norms. The decay rate in the mass super-critical regime is the same one as of \(e^{i \cdot \Delta} u_0\). This rate is different in the mass sub-critical regime, which requires some extra assumptions. The novelty here is the scattering of global solutions in the weighted conformal space for the class of source terms \(p_0<p<\frac{2-\rho}{N-2}+1\). This helps to better understand the asymptotic behavior of the energy solutions. Indeed, the source term has a negligible effect for large time and the above non-linear Schrödinger problem behaves like the associated linear one. In order to avoid a singular source term, one assumes that \(p \geq 2\), which restricts the space dimensions to \(N \leq 3\). In a paper in progress, the authors treat the same problem in the complementary case \(\rho<0\).