  We calculate the Picard groups for principal blocks $B$ with TI defect groups
and cyclic inertial quotient. The methods used generalize results on self
stable equivalences and take advantage of the existence of equivalences given
by Green correspondence in this setting. In particular, we show that
$\text{Pic}(B)=\mathcal{E}(B)$, giving more evidence for a conjecture on basic
auto-Morita equivalences.
