The problem of possible controlling the antihydrogen formation and deexcitation has become an actual one for the investigation of efficient methodologies for the production of cold antihydrogen in the ground state. In 1983–1997 it was suggested and discussed by A. Wolf the possibility of laser-stimulated formation and stabilization of antihydrogen in collisions of antiprotons with positrons. In the present report we analyze the question with a wave-packet propagation method developed for the quantum two-body problem with a non-separable interaction. This computational technique can also be applied for analyzing the laser-assisted antihydrogen formation in magnetic traps.