Mine (see that, Mine) is prewar. Serial number 197XXX.
I field stripped it last night. Interior of barrel shiny as new and just needed a few passes with brush and patches to get it clean enough for me. The forend (cracked) has a number stamped into the wood identical to the serial number on the receiver. I did not get the buttstock off (dog gone those FN/Browning screws has some thin slots - I ordered Brownell's "Auto 5" screw driver kits this morning) to see if it had a serial number somewhere.
I took some 0000 steel wool and 3n1 oil and started polishing. Man that thing cleaned up pretty. Green Tops graded is "Poor" condition. You would not believe how good it looks now. One spot of nasty pitting on the rear of the receiver but the rest of the receiver and barrel are now mostly a nice shiny blue. Not the blue of a new Browning but dog gone good for a 70+ year old gun. Even though I've ordered a synthetic stock/forend I'm going to work on the originals. Just need to strip'em and try my hand at some checkering refurbishment.
Also ordered a set of springs, friction rings, receiver and buttplate screws for it. Someone buggered up the screws some time in the past. I'll install the new ones when I completely strip it down and then try to repair the heads on the old screws if I can (spares).
I'm fighting the urge to take it down to the edge of the woods behind my house and cutting loose with 5 rounds.
