Consider the residual graph G_f
We first note the fact that once a graph has obtained its max flow there cannot be any s-t paths within in the residual graph as that means we still have yet to fully saturate all paths.
 Suppose A_o and B_1 non empty (if empty this is trivially true) and let u in A_o and v in B_1
Accordingly this means there is a forward path from s to u and v to t.
However since this is under max flow there cannot be a s-t path thus there is no forward edge between u and v.
Accordingly if we increase the capacity of edge (u,v) by one we create a forward edge between (u,v) with capacity 1, thus allowing one more flow thus increasing max flow by 1 and achieving G’ as desired.