In this work using the effective-mass approximation within a variational approach we study the effect of the 3D longitudinal optical phonons on the energy of a shallow donor impurity in a GaAs–(Ga,Al)As quantum-well wire with a magnetic field applied in the wire-axis direction. We obtain the energy of the lower impurity states as a function of the wire radius, the donor position inside the wire, and under the effect of the applied magnetic field. The polaron effects on the impurity energy are studied using second order perturbation theory. We include non-parabolicity effects to explain the optical experiments under applied high magnetic fields.