We prove that a distribution $T$ with an $S$-asymptotic related to $c(h)$ and to the cone $\Gamma$ has on the set $B+\Gamma$ a restriction which is a finite sum of derivatives of the functions $F_i$, continuous in $B+\Gamma$ and having some properties which imply that alle the $F_i(x+h)/c(h)$ converge uniformly for $x\in B$, when $h\in\Gamma$ and $\|h\|\to\infty$. If we know more about the distribution $T$ or about the cone $\Gamma$, then we can say more about the properties of $F_i, B$ is the ball $B(0, r)$.