The stocks are incorrect for a 1945 Remington Rand. They do not have reinforcement rings around the screw holes. You sound a bit unsure about some of the pistol details...like serial number and markings inside the stocks. That's why it is always a lot more helpful to simply post good images of the markings and details, then ask for comments. Someone new to the pistols will miss a lot of things and, in turn, report inaccurate information...thereby leaving us in the dark and unable to tell you what you may really have.