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If you had a paper based FP - 1-1.5 months.
If computer based - within 24 hours.
It has nothing to do with your state. After taking your FP, the information (FP) is forwarded to the FBI. If electronic, they run a quick scan and send the results to the RSC within 24 hours. If paper based, then that is a seperate process.
The INS does not update the system for a while after getting the info. For eg. my FP date was scheduled for 01/24/02 (NY, Bronx). I completed it on 01/12/02 (early). AVM changed that a notice was sent on 01/14/02. On calling FBI, they confirmed results were sent on 01/13/02. AVM changed on "received FP results and processing resumed" on 01/21/02.