Quantum-Informational Metric Genesis Cosmology (QIMG Cosmology) is proposed as a post-FRW extension of the Cyclic Black Hole Information Reintegration Theory (CBHIRT). While CBHIRT defines the pre-geometric informational initial conditions inherited from Page-time black-hole correlations, QIMG investigates how this inherited quantum-informational structure may be represented after FRW activation as an effective covariant geometric and stress-energy representation. The central aim of QIMG is to construct a mathematical bridge between quantum information theory and general relativity. The model does not claim that information is directly converted into physical energy. Instead, it proposes that a pre-geometric informational substrate, described by an informational field \(I(x^\mu)\), can determine the effective metric structure \(g_{\mu\nu}[I]\) and an informational stress-energy representation \(T^{\mathrm{info}}_{\mu\nu}[I]\) within the post-FRW layer. In this framework, dark matter is interpreted as an effective gravitational imprint of partially mapped informational structure, while dark energy is interpreted as an effective expansion term associated with time-dependent informational mapping. The framework introduces an informational metric-genesis relation, a covariant informational stress-energy tensor, a dynamic vacuum representation \(\rho_{\mathrm{vac}}(t)\), and modified perturbation equations describing how inherited informational structure may influence structure formation and cosmic expansion. These mathematical components allow QIMG to formulate testable dark-sector signatures, including scale-dependent structure-growth effects, possible deviations in the dark-energy equation of state, and high-redshift galaxy-formation pathways. QIMG therefore does not replace the CBHIRT ontology, nor does it modify general relativity at the fundamental level. Rather, it provides a post-FRW effective representation in which quantum-informational correlations can be translated into the language of metric geometry, effective stress-energy, and dark-sector phenomenology. In this sense, QIMG offers a formal pathway for connecting quantum information theory with general relativity while preserving the distinction between informational ontology and physical energy dynamics.