According to the SCS&W from the beginning of commercial production and continuing up to the mid or late 1970's S&W stocks were numbered to the gun to which they were originally fitted.
The guns serial number was marked on the right side grip and normally did not include the prefix. An exception was on some Victory's which did include the prefix.
From around 1900 to the late 1920's they used pencil to write the s/n. From about 1929 they began stamping the s/n and stamped one number at a time. Around the mid-1960s the stamping was changed from individually stamped numbers to a straight line stamping of the entire s/n alond the bottom of the right panel.
Here are the stocks from my 1947 K-22
and a set of post 1970 RBs
and from a 1924 .38 M&P (you can barely make out the pencil writing towards the top of the stock)