After you have filed your I-600A with the INS, the INS will send you an appointment for fingerprinting. How long you have to wait to get this appointment notice varies considerably. It will likely be somewhere in the two to four week range. An INS office will take the prints and send them to the FBI for processing.
The FBI processes the prints and notifies the INS if you pass or not. When we were processed in the fall of 1999, it took about a month for the FBI to process the prints. In September of 2002 it only took one working day! (Prints taken on a Friday, we were processed by the following Monday.).
At the time you expect your prints should have been processed, call the FBI Liason office to check on them. They only tell you if they have been processed, not if you passed. However, if they couldn't process your prints (usually due to not having a clear enough print) it will be weeks before the INS will tell you that. If you find you need to be reprinted, you can ask the INS to do that ASAP.
The FBI Liasion office number is:
(304) 625-5590.
They are open Mon-Fri, 8am to 11pm Eastern.
On the initial voice menu, you want to select "4" to check on fingerprints.
This is a toll call, there is no toll free number.