[en] The He⁺ ion on a plane subject to a constant magnetic field B perpendicular to the plane is considered taking into account the finite nuclear mass. Factorization of eigenfunctions permits to reduce the four-dimensional problem to three-dimensional one. The ground state energy of the composite system is calculated in a wide range of magnetic fields from B=0.01 up to B=100a.u. and center-of-mass Pseudomomentum K from 0 to 1000 a.u. using a variational approach. The accuracy of calculations for B=0.1a.u. is cross-checked in Lagrange-mesh method and not less than five significant figures are reproduced in energy. Similarly to the case of moving neutral system on the plane a phenomenon of a sharp change of energy behavior as a function of K for a certain critical K_c but a fixed magnetic field occurs