  We introduce $\bar G$-fusions of local pointed groups on a block extension
$A=b\mathcal{O}G$, where $H$ is a normal subgroup of the finite group $G$,
$\bar G=G/H$, and $b$ is a $G$-invariant block of $\mathcal{O}H$. We show that
certain Clifford extensions associated to these pointed groups are invariant
under group graded basic Morita equivalences.
