There are so so many theories regarding the possible answer to your question. This question has been discussed plenty of times in different forums on the internet. So I see no extra room to come up with my own theories. Some of the theories I found after hitting Google are:
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.
Several theory from the viewers:
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.!
It also explains that Allison Kerry, just before she died, was not surprised when she saw Amanda!!!
5) They found fingerprints of Amanda on Troy's body or something else of the classroom trap!
And another theory :)
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.
These are all great theories from Saw lovers. I have not stated any theories on my own. It is kind of a collection of theories, but I could not find any official response on it.
Although how the FBI knew that Amanda Young was an accomplice of Jigsaw, at this point in time this fact remains unexplained.