There are so so many theories regarding the possible answer to your question. This question has been discussed a plenty no of times in different forums in the internet. So I see no extra room to come up with my own theories. Some of the theories I found after hitting the 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 any one except the FBI ( Kerry was liason working for the FBI ).
3) In Saw 2 , after Daniel Matthews disappearance, when FBI started to investigate the Tape, they found 6 dead bodies and Daniel Matthews in the Safe, However the eight person was recognised 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 about Amanda when allison Kerry found him. And Allison kerry only told it to Peter Strahm and Lindsey Perez, That explains why she know that someone else was responsible for the death of Troy in Saw III.!
It also Explains that allison kerry just before she dies was not surprised about by seeing Amanda!!!
5) They found finger prints of amanda on Troy's body or something else of The Class Room Trap!
And another theory :)
6) I kinda think they found out through Daniel cause after they found him they must have take in him
to the hospital then interview him so he mentions Amanda's and him feeling hit in the back or something and then the FBI says maybe
she's an accomplice.
7) They watch a record from Saw-2. We can't see final of record, and I think they saw how Amanda drug Daniel and take his body from gas house. Saw-4 (when we know that FBI already know about Amanda) is far late than Saw-2, all the magazines wrote about Jigsaw, as we've seen)) So anyone in police and FBI know about Amanda.
These are all great theories from Saw lovers. I have not put any theory on my own. It is kind of collection of theories. But 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 remains unexplained