  In this paper we construct a homomorphism of the affine braid group
$Br_n^{aff}$ in the convolution algebra of the equivariant matrix
factorizations on the space $\overline{\mathcal{X}}_2=\mathfrak{b}_n\times
GL_n\times\mathfrak{n}_n$ considered in the earlier paper of the authors. We
explain that the pull-back on the stable part of the space
$\overline{\mathcal{X}_2}$ intertwines with the natural homomorphism from the
affine braid group $Br_n^{aff}$ to the finite braid group $Br_n$. This
observation allows us derive a relation between the knot homology of the
closure of $\beta\in Br_n$ and the knot homology of the closure of
$\beta\cdot\delta$ where $\delta$ is a product of the JM elements in $Br_n$
