There is a letter S at one end of the butt and then the serial number "934xxx" on the other end of the butt.
First, welcome to the Forum.
Second, you have an immediate postwar .38 Military & Police revolver. The S prefix was used only from March, 1946 (ship dates) until sometime in 1948. Actual stamping of the S prefix guns started in September, 1945 and stopped in March, 1948, when the serial sequence hit S999999. That one actually shipped to Minnesota in June, 1948.
The S sequence began at roughly S811xxx and was intermingled with SV prefix guns for a short while. Both the SV and S prefixes were used to wind up the serial sequence that began on April 24, 1942 with V1. In December, 1944, the S was added in front of the V to indicate an internal engineering change involving a new sliding hammer block safety mechanism. When wartime production stopped, the SV was phased out in favor of the simple S. When the S sequence ran out, it was replaced with the C prefix, in March, 1948.
Your particular example, S934xxx, very likely shipped in August, 1947, possibly September of that year. The M&P was a high volume shipper in that period, so most of them didn't hang around the factory for long after they were produced. Ship dates are quite consistent during this time, unlike during earlier and later periods. So we can usually guess pretty closely on ship dates for these guns (with only occasional outlying examples showing up).
I'm in the midst of a research project on these revolvers. I would greatly appreciate having the complete serial number for your gun. If you don't wish to post it openly, perhaps you would send it to me via PM. Ownership isn't tracked, just serials and features. If you can post some clear pictures here, it would also be appreciated. A pic of the left side is the most needed.
Regards, and thanks for posting.