We report novel efficient Mn4+ phosphors of composition K3HF2MO2F4:Mn4+ (M = Mo, W) containing [HF2]- and octahedral [MO2F4]2- building units. The phosphor exhibits strong absorption at 450 nm and an external quantum yield of 90%. K3HF2WO2F4:0.01Mn4+ provides a sufficiently high quenching temperature T1/2 of about 400 K and is applicable as a converter for (In,Ga)N LEDs. The EPR spectrum is consistent with the presence of a MnF62- species at giso = 1.983. 19F MAS NMR results confirm the 2 : 1 ratio of the metal-bound fluoride species to the hydrogen difluoride group as predicted from the chemical formula. There are two distinct M-bonded species in a 1 : 1 ratio, indicating that the W and Mo octahedra are exclusively of the MO2F42- type, with the two oxygen atoms in cis-position. Their extremely sharp 19F resonances indicate a fast, near-isotropic reorientational process at room temperature that is on the millisecond timescale. For the HF2- group, the 19F and 1H MAS NMR spinning sideband profiles reveal the geometry of a linear centrosymmetric three-spin system with an H-F bond distance of 1.14 Å.