Does the electrodynamics-like PDE $\epsilon^{ijk}\partial_j B_{kl}(x) = \delta^i_l\delta^{(3)}(x)$ have solutions?

Question

Consider the following PDE in 3 dimensions $$ \epsilon^{ijk}\partial_j B_{kl}(x) = \delta^i_l\delta^{(3)}(x)$$ Does $B_{kl}(x)$ have a solution? (It can have any kind of singularity, e.g. it can have singularity at the positive $z$ axis like a Dirac string emanating from the origin.)