Welcome to the forum.
Your SPORTSMAN DOUBLE ACTION revolver is a 7th Variation made in 1940 ('A' prefix indicates that year.) The Serial number is that found on the front strap of the grip frame. The partial serial number (usually without letter prefix) will be found on the left side of the grip frame, under the top strap, and three (sometimes 4) numbers on both the breech face of the cylinder and on the extractor star and most often on the upper barrel latching piece. Matching numbers in all those places indicates that the piece is all original. Many H&R revolvers of that era are seen with one, two or more letters stamped into both sides of the grip frame - those are most likely inspectors/installers marks applied at various steps of production. The inclusion of full or partial serial numbers on all main groups was done to keep individually hand fitted pieces together as a unit after final finishing.
If it shows "normal" wear and tear - I'm assuming maybe 80% finish remaining and all parts work as designed - your gun is currently RETAILING in the $225 to $265 range.
If you are lucky enough to find the "Rice" type, monogrip in wood - your best chance will be on one of the firearms on-line auction sites - they show up occasionally. I know of NO Pachmayr grip that will fit that firearm - the frame style was discontinued in 1952. BTW - the wooden grip will have the exact same contour as the nylon grip currently on your gun and attach in the same manner. Begining in 1940, the nylon/plastic monogrip began to replace checkered walnut grip of earlier variations and along with brown grips of the same composition became the standard issue during WW2.
Good luck - any other questions? Please ask.
Here's a pic of a 1940 with a checkered, walnut grip: