Let us calculate the prefix function for this string.

Now think about the meaning of the values of the prefix function, except for the first $n + 1$ entries (which belong to the string $s$ and the separator).

By definition the value $\pi[i]$ shows the longest length of a substring ending in position $i$ that coincides with the prefix.

But in our case this isisnothing more than the largest block that coincides with $s$ and ends at position $i$.

But in our case this is nothing more than the largest block that coincides with $s$ and ends at position $i$.

This length cannot be bigger than $n$ due to the separator.

But if equality $\pi[i] = n$ is achieved, then it means that the string $s$ appears completely in at this position, i.e. it ends at position $i$.

Just do not forget that the positions are indexed in the string $s +\\# + t$.