A ring $R$ is called a left APP-ring if the left annihilator $l_R\left(Ra\right)$ is right $s$-unital as an ideal of $R$ for any element $a\in R$. We consider left APP-property of the skew formal power series ring $R\left[\right[x;\alpha \left]\right]$ where $\alpha$ is a ring automorphism of $R$. It is shown that if $R$ is a ring satisfying descending chain condition on right annihilators then $R\left[\right[x;\alpha \left]\right]$ is left APP if and only if for any sequence $(b_0,b_1,\cdots )$ of elements of $R$ the ideal $l_R$$...$