  Given a holomorphic line bundle $L$ on a compact complex torus $A$, there are
two naturally associated holomorphic $\Omega_A$--torsors over $A$: one is
constructed from the Atiyah exact sequence for $L$, and the other is
constructed using the line bundle $(p^*_1 L^*)\otimes (\alpha^*L)$, where
$\alpha$ is the addition map on $A\times A$, and $p_1$ is the projection of
$A\times A$ to the first factor. In \cite{BHR}, it was shown that these two
torsors are isomorphic. The aim here is to produce a canonical isomorphism
between them through an explicit construction.
