Unveiling the impact of trivalent metal cation transmutation on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Cs</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>AgM</mml:mi> <mml:mo>(</m

Lead-free halide double perovskites ${A}_{2}M(\mathrm{I})M(\mathrm{III}){X}_{6}$ have garnered significant attention in the past decade as promising alternatives to $\mathrm{CsPb}{X}_{3}$ perovskites, addressing concerns related to lead toxicity and material instability. In this work, we employ a trivalent metal cation transmutation strategy to design a series of inorganic Pb-free halide double perovskites ${\mathrm{Cs}}_{2}\mathrm{Ag}M(\mathrm{III}){\mathrm{Cl}}_{6}$ and perform a comprehensive investigation into their potential for applications in optoelectronic devices. Our first-principles calculations, rooted in density functional theory, demonstrate that these materials possess a face-centered cubic lattice structure while showcasing remarkable thermodynamic, dynamical, and mechanical stability. The ${G}_{0}{W}_{0}$@PBE electronic band gap ranges from 1.47 to 6.20 eV, while the Bethe-Salpeter equation (BSE) indicates strong optical absorption spanning near-infrared to ultraviolet regions for these compounds. Furthermore, the excitonic properties suggest that these perovskites exhibit intermediate exciton binding energies (0.17 to 0.60 eV) and generally longer exciton lifetimes, except for the materials with $M$(III) = Sc, Y, Tb, and Lu. The Fr"ohlich model indicates that these materials exhibit intermediate to strong carrier-phonon interactions, with hole-phonon coupling more prominent than electron-phonon coupling. Interestingly, the charge-separated polaronic states are found to be less stable than the bound exciton states, with higher polaron mobility for electrons ($4.92--29.03\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{2}{\mathrm{V}}^{\ensuremath{-}1}{\mathrm{s}}^{\ensuremath{-}1}$) than for holes ($0.56--8.69\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{2}{\mathrm{V}}^{\ensuremath{-}1}{\mathrm{s}}^{\ensuremath{-}1}$) in these materials. Overall, our study demonstrates that trivalent metal cation transmutation in ${\mathrm{Cs}}_{2}\mathrm{Ag}M(\mathrm{III}){\mathrm{Cl}}_{6}$ enables the creation of stable and lead-free halide double perovskites with exceptional, tunable optoelectronic properties, making them ideal for flexible optoelectronic applications.