Many signature schemes use forking lemma to prove security, like scheme in here.In short, that goes through a reduction technique which called oracle-replay attack to solve the difficult algorithmic problem, requiring two rounds of simulation for $\mathcal{F}$ to obtain two valid signature pairs $(m,r,e,s)$ and $(m,r,e',s')$,where $r$ is a "commitment", $e = H(m||r)$,$s$ and $s'$ is related to $m$, $r$ and $e$. But how to ensure the forger $\mathcal{F}$ will output the same message $m$ and $r$ ,since they may select randomly in each simulation?
see also [PS00] David Pointcheval and Jacques Stern. Security arguments for digital signatures and blind signatures. Journal of Cryptology, 2000.