I don't use MFC, but you can probably translate to what you need. The issue is you need to send the message to the edit control, not the main window.
#include <Windows.h>
#include <string>
#include <cstdlib>
int main()
{
const std::string data("This is some text from the clipboard.");
HGLOBAL hMem = GlobalAlloc(GMEM_MOVEABLE, data.size() + 1);
std::memcpy(GlobalLock(hMem), data.c_str(), data.size() + 1);
GlobalUnlock(hMem);
OpenClipboard(NULL);
EmptyClipboard();
SetClipboardData(CF_TEXT, hMem);
CloseClipboard();
HWND mainWindow = FindWindow(NULL, "Untitled - Notepad");
HWND editWindow = FindWindowEx(mainWindow, NULL, "edit", NULL);
PostMessage(editWindow, WM_PASTE, 0, 0);
return 0;
}