Factor-representation of the group $GL(\infty)$ and admissible representations $GL(\infty)^X$

This article is the second part of the work in which classification of factor-representations of group $GL(\infty)$ is given. The criterium of unitary equivalence of spherical representations of the group $(GL(\infty)^X)$ functions on finite set $X$ with values in $GL(\infty)$ in terms of their parameters is received here. A conformity between factor-representations of group $GL(\infty)$ and spherical representations of group $(GL(\infty)^X)$ is constructed. The design of continuation on the group of motions which corresponds to group $(GL(\infty)^X)$ is given for the received spherical representations.