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The charge states and lattice sites of Fe ions in both virgin and Mn-doped Al$_x$Ga$_{1-x}$N samples have been investigated by employing $^{57}$Fe emission Mössbauer spectroscopy (eMS) using radioactive $^{57}$Mn$^+$ ion implantation at ISOLDE, CERN. In undoped Al$_x$Ga$_{1-x}$N, Fe$^{2+}$ ions occupying Al/Ga lattice sites associated with nitrogen vacancies, as well as substitutional Fe$^{3+}$ ions, have been identified. Upon Mn doping, a substantial suppression of the Fe$^{3+}$ signal is observed. This is accompanied by the emergence of a single-line component, attributed to Fe$^{4+}$ ions on Al/Ga sites that are enabled by the presence of nearby substitutional Mn$^{2+}$ ions. The experimental results are supported by density functional theory calculations. This work establishes co-doping as a new avenue for tailoring magnetic properties in doped III-nitride semiconductors.