The acceptor-related photoluminescence of a GaAs–(Ga,Al)As superlattice, under the influence of a magnetic field applied parallel to the interfaces, is theoretically studied following a variational procedure within the effective-mass approximation. Electron and hole magnetic Landau levels and envelope wave functions were obtained by an expansion in terms of sine functions, whereas for the impurity levels the envelope functions were taken as products of sine and hydrogenic-like variational functions. Impurity binding energies and wave functions are obtained for acceptors at a general position in the superlattice and for different in-plane magnetic fields. Theoretical results corresponding to transitions from the conduction subband to states of acceptors (miniband-to-acceptor e−A0 transitions) at the edge and center positions of the GaAs quantum well compare well with available experimental data by Skromme et al. [Phys. Rev. Lett. 65, 2050 (1990)] on the magnetic-field dependence of the photoluminescence peak position of conduction miniband-to-acceptor transitions for different temperatures and values of the superlattice period.