The preceding post is generally correct. Smith & Wesson resumed production of their commercial Military & Police revolvers in September, 1945 at serial number S 811,120. The "S" denoted that the revolver had a new positive hammer block, and could be carried fully loaded with 6 rounds. Your revolver would then be the 136,647th of several million made after World War Two.
In addition, your Grandfather’s revolver is a relative scarce variant called a “transitional”. In 1948 S&W introduced a new style of lockwork, called a “short action,” at serial number S 990,184. This shortened the cocking stroke of the hammer somewhat, but at the expense of a light, ultra-smooth double-action trigger pull that was prized by many shooters and law enforcement officers. Those revolvers made between serial numbers S 811,120 to approximately S 990,184 had the earlier pre-war “long action,” along with the new hammer block, which was a unique combination.
Given this gun's history within your family, I suggest that you do get it "lettered." To do so you will need a snapshot of the gun, a full description including the serial number on the butt, and a check in the amount of $30.00 made out to Smith & Wesson. In exchange the company's historian, Roy G. Jinks, will research the original records (which are not computerized by the way) and send you a letter containing the details of what he finds.
This comprehensive document will contain an overview of the model’s history, followed by the details of your particular gun. This usually includes the caliber, barrel length, finish, and the exact date it was shipped from the factory, and to what distributor or dealer. If there are any special features they will be listed too. This information is often invaluable to both you and future generations because you will have positive proof of its history and authenticity, for what is a modest fee. Other companies charge up to $100.00 and more for this kind of information.
Additional information on a historical letter will be found at the Smith & Wesson company website at:
www.smith-wesson.com