  In a recent paper here arXiv:1508.0005 it is shown that irreducible
representations of the three string braid group $B_3$ of dimensions $\leq 5$
extend to representations of the 3-component loop braid group $LB_3$. Further,
an explicit $6$-dimensional irreducible $B_3$-representation is given that does
not extend. In this note we give a necessary and sufficient condition, in all
dimensions, on the components of irreducible representations of the modular
group $\Gamma$ such that sufficiently general representations extend to $\Gamma
\ast_{C_3} S_3$. As a consequence, the corresponding irreducible
$B_3$-representations do extend to $LB_3$.
