Photodetachment microscopy of monovalent anions is studied theoretically with a uniform transverse magnetic field $\vec{B}$ superimposed to the electric field $\vec{E}$ . The main experimental results given by Chaibi et al. (EPL, 82 (2008) 20005) have been reproduced using the closed-orbit theory, and confirmed through the quantum source theory with the energy Green function evaluated by means of the stationary phase approximation. Both theoretical methods yield consistent descriptions of the electron flux distribution for all field intensities and angular momentum of electrons we studied. Our calculations show that the presence of the magnetic field leads to a global displacement of the ring patterns along the $\vec{E}\times\vec{B}$ -direction, confirming the experimental observations under weak magnetic-field conditions. In addition, we found that the shape and size of the interference patterns change from circular to elliptical as the magnetic field increases.