 Collinear inelastic capture followed by two photons

In an isolated collinear completely inelastic capture, add incoming total energies and signed momenta. Their invariant fixes the composite rest mass, including internal excitation. If it later converts all energy to two opposite axial photons, the two conservation equations immediately give the displayed photon energies. The laboratory frequency ratio is $(E+Pc)/(E-Pc)$, not generally one; equality holds in the composite rest frame.