  We generalize Ng's two-variable algebraic/combinatorial $0$-th framed knot
contact homology for framed oriented knots in $S^3$ to knots in $S^1 \times
S^2$, and prove that the resulting knot invariant is the same as the framed
cord algebra of knots. Actually, our cord algebra has an extra variable, which
potentially corresponds to the third variable in Ng's three-variable knot
contact homology. Our main tool is Lin's generalization of the Markov theorem
for braids in $S^3$ to braids in $S^1 \times S^2$. We conjecture that our
framed cord algebras are always finitely generated for non-local knots.
