  We present a very natural but yet useful criterion to detect vanishing of
essential algebras of a Green biset functor $A$ by means of morphisms. We
introduce the morphisms $Inf:A \rightarrow A_G$ and $Res:A_G\rightarrow A$ to
prove that the class of groups for which the essential algebras do not vanish
is the same for $A$ and any shifted functor $A_G$. We use the kernel of $Res$
to give a characterization of the seeds of simple $A_G$-modules which are not
obtained as pullback of simple $A$-modules.
