macOS has several great screenshot methods, including built-in keyboard shortcuts and a third-party app. These may be very useful; I have recently found a new way which you can easily take screenshots of the login window on macOS Ventura, Monterey, Big Sur, Catalina and macOS Capitan.
This seems to be a new function of El Capitan or above, because I cannot perform these actions on Mac OS X Yosemite or Mavericks.
How to take a screenshot of login windows by using keyboard shortcuts
At Login screen of your Mac interface: Taking a screenshot of the whole login window, just press: Command + Shift + 3.
Taking a screenshot of a part of the login window, just press: Command + Shift + 4.
When you log in on a Mac, the login window screen capture will be saved to the Desktop with the name beginning with LW.
Example: LWScreenShot 2015-11-02 at 6.36.33 AM, LWScreenShot 2015-11-02 at 7.25.55 AM
If you want to change the default location for saved screenshots, you can see this guide at this post.