  The $\Lambda$ $\to$ $\Sigma^0$ transition magnetic moment is computed in the
QCD sum rules approach. Three independent tensor structures are derived in the
external field method using generalized interpolating fields. They are analyzed
together with the $\Lambda$ and $\Sigma^0$ mass sum rules using a
Monte-Carlo-based analysis, with attention to OPE convergence, ground-state
dominance, and the role of the transitions in the intermediate states.
Relations between sum rules for magnetic moments of $\Lambda$ and $\Sigma^0$
and sum rules for transition magnetic moment of $\Lambda$ $\to$ $\Sigma^0$ are
also examined. Our best prediction for the transition magnetic moment is
$\mu_{\Sigma^0\Lambda}= 1.60\pm 0.07\; \mu_N$. A comparison is made with other
calculations in the literature.
