The total cross section for single electron capture from He by Li³⁺ ions has been calculated using the close-coupling technique in the impact energy range 1.5*10^-4-43 keV. The model-potential method was used to determine the electronic energy curves of the (LiHe)³⁺ molecule. The dynamic couplings between the molecular states were obtained by numerical differentiation of the model-Hamiltonian stationary wavefunctions. Depending on the impact energy, the collision dynamics were solved either by a full quantum-mechanical treatment or using the semiclassical impact parameter approximation. The total charge exchange cross section is in good agreement with the experimental results of Wirkner-Bott et al. (1981).