Costello's theorem,"open TCFT=Calabi Yau A-infinity category",he also mentions when applied to Fukaya category we can recover Gromov-Witten theory, but I see that it needs some assumption,also even if the assumption is true,I just see that the TCFT associated to Fukaya category is the same as the one associated to Gromov-Witten invariant, BUT can we from that TCFT to RECOVER Gromov-Witten invariants? (I mean the opposite direction) Because otherwise,it is not A model.

I appreciate if there is any answer.