  The first two steps of the construction of motivic integration in the
fundamental work of Hrushovski and Kazhdan have been presented in
arXiv:1006.2467v1. In this paper we present the final third step. As in
arXiv:1006.2467v1, we limit our attention to the theory of algebraically closed
valued fields of pure characteristic 0 expanded by a (VF, \Gamma)-generated
substructure S in the language L_{RV}. A canonical description of the kernel of
the lifting map is obtained.
