For the case of two particles a solution of the string field theory vertex axioms can be factorized into a standard form factor and a kinematical piece which includes the dependence on the size of the third string. In this paper we construct an exact solution of the kinematical axioms for which includes all order wrapping corrections w.r.t. the size of the third string. This solution is expressed in terms of elliptic Gamma functions and ordinary elliptic functions. The solution is valid at any coupling and we analyze its weak coupling, pp-wave and large L limit.