Recently, a new perturbative QCD factorization formalism for heavy quarkonium production at a large transverse momentum was proposed. Phenomenological application of this new approach relies on our knowledge of a large number of universal fragmentation functions (FFs) at an input factorization scale with heavy quark mass , which are nonperturbative, and in principle, should be extracted from data. With heavy quark mass , we calculate these input FFs in terms of non-relativistic QCD (NRQCD) factorization. In a companion paper, we calculated these input FFs in NRQCD factorization approach including all contributions from -wave NRQCD -states. In this paper, we calculate contributions to the heavy quark-pair FFs from all -wave NRQCD -states.