  The Heisenberg group $\mathbb{H}^1$ is known to be conformally equivalent to
the CR sphere $\mathbb{S}^3$ minus a point. We use this fact, together with the
knowledge of the tangential Cauchy-Riemann operator on the compact CR manifold
$\mathbb{S}^3$, to solve the corresponding operator on $\mathbb{H}^1$.
