Maxwell's curl equations and the linearized balance equations for momentum and pressure tensor for a plasma in an external magnetic field are combined in a system of first-order partial differential equations for the field quantities. With the corresponding adjoint system, the Lagrange identity is established, leading to a symmetry relation between the Green functions for the original and the adjoint fields. With temporal mapping the adjoint field can be transformed into a ‘Lorentz-adjoint’ (physical) field, leading to a reciprocity relation between the Green functions for the original and for the Lorentz-adjoint fields.