The fully differential cross section for the positron- and electron-impact ionization of H₂ is calculated. For positron impact the results are contrasted against a recent experiment which evidently shows the in uence of the electron capture to a low-lying positronium continuum state. From a detailed analysis it is deduced that the capture probability is dependent on the orientation of the electron-positron relative momentum vector with respect to the residual ion. Within the used model, this asymmetric positronium formation is traced back to the distortion of the positron motion by the two-center potential formed by the residual ion and the secondary electron.