  Asymptotic expressions for the radial and full wave functions of a three{body
bound halo nuclear system with two charged particles in relative coordinates
are obtained in explicit form, when the relative distance between two particles
tends to infinity. The obtained asymptotic forms are applied to the analysis of
the asymptotic behavior of the three-body (pn?) wave functions for the halo
($E^*=3.562$ MeV, $J^{\pi}=0^+$, $T=1$) state of $^6$Li derived by D. Baye
within the Lagrange-mesh method for two forms of the $\alpha N$ -potential. The
agreement between the calculated wave function and the asymptotic formula is
excellent for distances up to 30 fm. Information about the values of the
three-body asymptotic normalization functions is extracted. It is shown that
the extracted values of the three-body asymptotic normalization function are
sensitive to the form of the $\alpha N$ -potential. The mirror symmetry is
revealed for the three-body asymptotic normalization functions derived for the
isobaric ($^6$He, $^6$Li) pair.
