The dynamics of high energy electrons in gyroresonance with a quasi-monochromatic circularly polarized whistler mode tracing a geomagnetic field line are studied numerically. The wavenumber and amplitude of the whistler wave are assumed to be slowly varying functions due to the weak longitudinal inhomogeneity of the geomagnetic field. The space-time dependence of the electromagnetic field manifests itself in the existence of an approximate invariant of the electron motion. Under the conditions characteristic of the magnetosphere, this invariant is found to be conserved with very high accuracy even in the process of resonant wave-particle interaction, whereas the constancy of the electron magnetic moment is strongly violated in the resonance. The availability of the approximate constant of the motion allows one to describe the gyroresonant wave-particle interaction with the aid of simpler equations averaged over the fast Larmor gyration.