In this note we prove the following Theorem – Let $X$ and $Y$ be two pointed CW complexes such that (i) $\overline {H}^*(X;\mathbb {F}_2)\simeq \Sigma ^2I$, where $I$ is an injective unstable module (ii)$\overline {H}^*(Y;\mathbb {F}_2)$ is gradually finite and nil-closed. Then the Adams spectral sequence for the group $[S^\infty X,S^\infty Y]$ degenerates at the $E_2$ term. This theorem is deduced by Lannes and the author, and from the relationship between the Ext groups and the derived functors of the destabilization.