  We present kinematically complete theoretical calculations and experiments
for transfer ionization in H$^++$He collisions at 630 keV/u. Experiment and
theory are compared on the most detailed level of fully differential cross
sections in the momentum space. This allows us to unambiguously identify
contributions from the shake-off and two-step-2 mechanisms of the reaction. It
is shown that the simultaneous electron transfer and ionization is highly
sensitive to the quality of a trial initial-state wave function.
