  We prove that for every group $G$ and any two sets $I,J$, the Brandt
semigroup algebras $\ell(B(I,G))$ and $\ell(B(J,G))$ are Morita equivalent with
respect to the Morita theory of self-induced Banach algebras introduced by
Gronbaek. As applications, we show that if $G$ is an amenable group, then for a
wide class of Banach $\ell(B(I,G))$-bimodules $E$, and every $n>0$, the bounded
Hochschild cohomology groups $H^n(\ell(B(I,G)),E^*)$ are trivial, and also, the
notion of approximate amenability is not Morita invariant.
