Asymptotic analysis of distributions in the problems with two boundaries. II

Let the conditions of the first part of the paper are satisfied. We obtain the complete asymptotic expansions of the probabilities
\begin{gather*} \mathbf P\{S_n=k,\,N>n\},\qquad k\in(-a,b),\\ \mathbf P\{S_N=k,\,N=n\},\qquad k\notin(-a,b), \end{gather*}
for the case $a=a(n)=o(n)$, $b=b(n)=o(n)$, $a\to\infty$, $b\to\infty$, $a+b\ge Cn^{1/2}$.