The probabilities and cross sections for the 1s² ¹S → 2s² ¹S and 1s² ¹S → 2s2p ¹P transitions induced in collisions of fast charged projectiles with helium atoms have been investigated in the framework of the operator approach to the few-body problem (V A Sidorovich, Physica Scripta, accepted for publication). Calculations have been performed for the case of the 2s² ¹S excitation of helium by projectiles with Z_p varying from 3 to 9 at collision energy E_p = 1.5 MeV/u. The calculated cross sections are in satisfactory agreement with the available experimental data. The cross section dependence upon the projectile charge is established. The wavefunctions for few-electron atom, satisfying the boundary condition U = 0 (U is the interconfiguration interaction potential) in the past or in the future, and the closure relation for joint system functions are presented.