A rapid and relatively simple scheme of calculation is elaborated and applied to cosmological recombination of helium. Employing the nonrelativistic Coulomb Green’s function, a wavefunction of a colliding electron is represented in an integral form applicable for calculations. Bound electrons of helium are described by the Hartree-Fock wavefunctions. The free-bound transition probabilities into excited states of helium and the probabilities of bound-bound transitions in helium are calculated in different modes. It is revealed that free-bound transition probabilities weakly depend on to what extent a field experienced by a colliding electron deviates from the purely Coulomb field with charge , whereas these probabilities strongly depend on the choice of a wavefunction of a bound active electron involved in recombination.