  We show that the Green correspondence induces an injective group homomorphism
from the linear source Picard group $\mathcal{L}(B)$ of a block $B$ of a finite
group algebra to the linear source Picard group $\mathcal{L}(C)$, where $C$ is
the Brauer correspondent of $B$. This homomorphism maps the trivial source
Picard group $\mathcal{T}(B)$ to the trivial source Picard group
$\mathcal{T}(C)$. We show further that the endopermutation source Picard group
$\mathcal{E}(B)$ is bounded in terms of the defect groups of $B$ and that when
$B$ has a normal defect group $\mathcal{E}(B)=\mathcal{L}(B)$. Finally we prove
that the rank of any invertible $B$-bimodule is bounded by that of $B$.
