Let $F$ be an algebraically closed field of prime characteristic $p$, let $H$ be a finite group and let $K$ be a normal subgroup of $H$. Let $B$ be a block of the group algebra $FK$, and let $A$ be a block of $FH$ covering $B$. We are interested in the question under what conditions $A$ and $B$ are Morita equivalent. We define a special type of Morita equivalence and show that $A$ and $B$ are equivalent in this way if and only if they have the same defect and $H$ acts by inner automorphisms on $B$. In case $B$ is $G$-stable this condition is satisfied for $A$ and $B$ if and only if it is satisfied for their Brauer correspondents.