When you connect an external monitor to your laptop it can happen that the Gnome login screen (GDM) is not shown on the monitor that you expect. To fix this do the following.
Step 1: Configure your monitor layout
Go into Gnome Settings and go to the Displays section. Now configure how you want to use your displays. Either use a single display or if you want to use multiple, make sure you set the correct primary monitor.
Step 2: Make it persistent for the login screen
Run the following commands to make the chosen setup is applied to the login screen. This copies your current configuration to the gdm user, which is the user under which the login screen is running.
sudo cp -v ~/.config/monitors.xml /var/lib/gdm/.config/ sudo chown gdm:gdm /var/lib/gdm/.config/monitors.xml