  All Killing symmetries in complex $\mathcal{H}$-spaces with $\Lambda$ in
terms of the Pleba\'nski - Robinson - Finley coordinate system are found. All
$\mathcal{H}$-metrics with $\Lambda$ admitting a null Killing vector are
explicitly given. It is shown that the problem of non-null Killing vector
reduces to looking for solution of the Boyer - Finley - Pleba\'nski (Toda
field) equation
