  In order to probe electron wave functions involved in the bonding of NH$_4$F,
we have performed Compton scattering experiments in an oriented single crystal
and in a powder. Ab initio calculations of the Compton profiles for NH$_4$F and
NH$_4$Cl are used to enlighten the nature of the bonds in the NH$_4$F crystal.
As a consequence, we are able to show significant charge transfer in the
ammonium ion which is not observable using other methods. Our study provides a
compelling proof for hydrogen bond formation in NH$_4$F.
