The response of a multiconfiguration self-consistent field wavefunction to a homogeneous periodic field is used to study the dipole hyperpolarizability of FH. All the tensor components are obtained for the second harmonic generation process for the ruby laser frequency and vibrational averaging is performed. Various contributions, which have been only estimated until now, were thus explicitly calculated. The final result, -7.8 au, is in agreement with previous theoretical estimates, but in disagreement with the experimental value.