Does a collision oracle for the pigeonhole subset sum problem produce solutions?
The way I understand it is the following.

Note that for $s_1$, $f_\vec{a'}(s_1)=T$  (because the sum was $T'$ and we replaced $a_j$ with $a'_j$ and we know that $j\in s_1$.

Now, they search for a collision, i.e., another $s_2$ such that $j\notin s_2$,
but $f_\vec{a'}(s_2)=T$. (is there a typo there, having $T'$ instead?)
Now, what is $f_\vec{a}(s_2)$? also $T$, right? since $j\notin s_2$...

Does it help?