  This is the second part of our ongoing project on the relations between
Gopakumar-Vafa BPS invariants (GV) and quantum K-theory (QK) on the Calabi--Yau
threefolds (CY3). We show that on CY3 a genus zero quantum K-invariant can be
written as a linear combination of a finite number of Gopakumar--Vafa
invariants with coefficients from an explicit ``multiple cover formula''.
Conversely, GV can be determined by QK in a similar manner. The technical heart
is a proof of a remarkable conjecture by Hans Jockers and Peter Mayr.
  This result is consistent with the ``virtual Clemens conjecture'' for the
Calabi--Yau threefolds. A heuristic derivation of the relation between QK and
GV via the virtual Clemens conjecture and the multiple cover formula is also
given.
