Positronium formation in the ground state and in a number of excited s states including the asymptotic n to infinity has been studied for the reaction e⁺+H₂ to Ps(ns)+H₂⁺ in the molecular Jackson-Schiff approximation (1953) in the energy range 50-1000 eV. It is found that the molecular effects play a significant role in the case of Ps formation and a hydrogen molecule cannot be considered as a pair of independent hydrogen atoms at any energy. The excited-state formation cross sections satisfy an n^-3 law approximately. It is also found that Ps formation involving the gerade transition of H₂⁺⁺ is the dominant process, although depending on the choice of molecular wavefunction there is a 10-28% probability of Ps formation involving the ungerade transition.