JQK
She should wait for him to sign then take the divorce agreement. Hopefully, she will live with her freedom peacefully and forget that man entirely. If in the end she will forgive him and be together again, I wouldn't know what to say then.
I agree, how foolish to leave it to him to sign & bring it later rather than demand he sign on the spot to take it with her. But, these plots sometimes use the excuse of drawn out divorce process to have the couple reconcile (depressingly ... I hope she gets rid of him so he can wallow in regret for being gullible to others that he could not see how geniune and sincere his own wife was)