I understand Parker was the one of the first, if the not the first to introduce them for their skeet and trap guns.
The "bulky fore-end" of the Parker SBT was standard from the intro in about 1915 (all the ads show the non-splinter fore-end and a straight grip and no safety). This was a dedicated trap gun.
Quoting myself from Parker Guns: The "Old Reliable"
@ p.71: "The beaver-tail or trap-style fore-end became an extra-cost option in 1923, probably due to the demands of Parker's modern trapshooting clientele." My research was to Parker advertising, catalogs, flyers, etc. The Parker Story
published the actual production records, and may move this date slightly back, but I'll stick with 1923 until I hear otherwise. It is doubtful that Parker was first, and the first Parker beaver-tails were defective in-so-far as they were too much wood to grip with too little metal structure. This was quickly corrected with the large screw seen at the front of the BTFE, which braces the wood internally to the barrel clasp. There may have been a recall, as I have never seen a factory original BTFE without the metal bracing screw. EDM