  In "Proof of the Arnold chord conjecture in three dimensions I", we deduced
the Arnold chord conjecture in three dimensions from another result, which
asserts that an exact symplectic cobordism between contact three-manifolds
induces a map on (filtered) embedded contact homology satisfying certain
axioms. The present paper proves the latter result, thus completing the proof
of the three-dimensional chord conjecture. We also prove that filtered embedded
contact homology does not depend on the choice of almost complex structure used
to define it.
