Existem tantas teorias sobre a possível resposta à sua pergunta. Esta questão foi discutida muitas vezes em diferentes fóruns na internet. Então não vejo espaço extra para criar minhas próprias teorias. Algumas das teorias que encontrei depois de atingir o Google são:
1) During Saw IV, Amanda's ability to pick up the much heavier Allison Kerry's unconscious body into her trap near the beginning of the previous movie is questioned by the FBI, leading them to suspect that there may be a second Jigsaw apprentice. It is unknown how the FBI knew that Amanda was in fact an accomplice to Jigsaw at the time. It is most likely that Hoffman had previously revealed it to the departments to cover up the fact that he was an apprentice as well.
Várias teorias dos espectadores :
2) Kerry told about Amanda after Daniel told her, but she never talked about it with anyone except the FBI (Kerry was liason working for the FBI).
3) In Saw 2 , after Daniel Matthews' disappearance, when the FBI started to investigate the Tape, they found 6 dead bodies and Daniel Matthews in the Safe, However the eighth person was recognized as Amanda Young, when they could not track her, they came to conclusion that Amanda Young was the accomplice to Jigsaw.
4) Daniel Matthews told Amanda when Allison Kerry found him. And Allison Kerry only told it to Peter Strahm and Lindsey Perez, That explains why she knew that someone else was responsible for the death of Troy in Saw III.!
Também explica que Allison Kerry, pouco antes de morrer, não ficou surpresa quando viu Amanda !!!
5) They found fingerprints of Amanda on Troy's body or something else of the classroom trap!
6) I kinda think they found out through Daniel because after they found him they must have taken him to the hospital and then interviewed him, so he mentions Amanda and his feeling hit on the back. Then the FBI says, maybe she's an accomplice.
7) They watch a record from Saw 2. We can't see the end of the record, and I think they saw how Amanda drugged Daniel and took his body from the gas house. Saw 4 (when we know that FBI already knew about Amanda) is far later than Saw 2. All the magazines wrote about Jigsaw, as we've seen. So the police and FBI know about Amanda.
Todas essas são ótimas teorias dos amantes da serra. Eu não afirmei nenhuma teoria por conta própria. É uma espécie de coleção de teorias, mas não encontrei nenhuma resposta oficial sobre isso.
Wikipedia declara:
Although how the FBI knew that Amanda Young was an accomplice of Jigsaw, at this point in time this fact remains unexplained.