The local structure and optical and vibrational properties associated with Mn2+-doped cubic AMF3 (A = K, Rb; M = Mg, Zn, Cd) fluoroperovskites are studied by means of embedding calculations using Kohn–Sham equations with constrained electron density. It is shown that while an electronic parameter like 10Dq essentially depends on the Mn2+–F− distance, the local vibration frequencies ωi (i = a1g, eg modes) are dominated by the interaction between F− ligands and nearest M2+ ions lying along bonding directions. The high ωa values observed for KMgF3:Mn2+ and KZnF3:Mn2+, the huge variations of ωe and ωa frequencies when the host lattice is changed, as well as the increase of Huang–Rhys factors and the Stokes shift following the host lattice parameter, are shown to be related to this elastic coupling of the MnF64− complex to the rest of the host lattice. The present results support the conclusion that the Stokes shift is determined by the interaction of the excited 4T1g state with a1g and eg local modes while the coupling with the t2g shear mode is not relevant. The variations of local vibrational frequencies and the Stokes shift induced by a hydrostatic pressure on a given system are shown to be rather different to those produced by the chemical pressure associated with distinct host lattices.