Automatic Essential morphisms

Question

Let $f:A\to\mathbb{K}(E)$ be a morphism of $C^*$-algebras, where $E$ is a Hilbert $B$-module. Define $E_1:=f(A)E\subset E$. Then $f$ can be considered as a map to $\mathbb{K}(E_1)$. My question is now, why is this map essential, that is there exists an approximate unit for $\mathbb{K}(E_1)$ in $f(A)$. Can anybody help?