FindWindow does not find the a window

 HWND Find = ::FindWindowEx(0, 0, "MozillaUIWindowClass", 0);

You need to use the full name of the application (as seen in Windows Task Manager -> Application tab)

Example:

Google - Mozilla Firefox

(after opening a Google tab in Firefox)

According to MSDN

lpWindowName [in, optional]

Type: LPCTSTR

The window name (the window's title). If this parameter is NULL, all window names match.

Thus your WindowName can't be "Mozilla Firefox", because the Firefox window's title is never "Mozilla Firefox" but it could be "Mozilla Firefox Start Page - Mozilla Firefox" or something depends on the web page's name. Here is the example picture

Thus your code should be like this, (the code below only work - only work if you have the exact window's title name: "Mozilla Firefox Start Page - Mozilla Firefox" like the image above. I have tested on Windows 8.1 and it worked)

void CaptureWindow()
{


RECT rc;
HWND hwnd = ::FindWindow(0, _T("Mozilla Firefox Start Page - Mozilla Firefox"));//::FindWindow(0,_T("ScreenCapture (Running) - Microsoft Visual Studio"));//::FindWindow(0, _T("Calculator"));//= FindWindow("Notepad", NULL);    //You get the ideal?
if (hwnd == NULL)
{
    return;
}
GetClientRect(hwnd, &rc);

//create
HDC hdcScreen = GetDC(NULL);
HDC hdc = CreateCompatibleDC(hdcScreen);
HBITMAP hbmp = CreateCompatibleBitmap(hdcScreen,
    rc.right - rc.left, rc.bottom - rc.top);
SelectObject(hdc, hbmp);

//Print to memory hdc
PrintWindow(hwnd, hdc, PW_CLIENTONLY);

//copy to clipboard
OpenClipboard(NULL);
EmptyClipboard();
SetClipboardData(CF_BITMAP, hbmp);
CloseClipboard();

//release
DeleteDC(hdc);
DeleteObject(hbmp);
ReleaseDC(NULL, hdcScreen);

//Play(TEXT("photoclick.wav"));//This is just a function to play a sound, you can write it yourself, but it doesn't matter in this example so I comment it out.
}

FindWindow only finds the window if it has the exact specified title, not just a substring.

Alternatively you can:

---

search for the window class name:

HWND hWnd = FindWindow("MozillaWindowClass", 0);

---

enumerate all windows and perform custom pattern searches on the titles:

BOOL CALLBACK EnumWindowsProc(HWND hwnd, LPARAM lParam)
{
    char buffer[128];
    int written = GetWindowTextA(hwnd, buffer, 128);
    if (written && strstr(buffer,"Mozilla Firefox") != NULL) {
        *(HWND*)lParam = hwnd;
        return FALSE;
    }
    return TRUE;
}

HWND GetFirefoxHwnd()
{
    HWND hWnd = NULL;
    EnumWindows(EnumWindowsProc, &hWnd);
    return hWnd;
}