At first I had to enter name and password blind, then the screen was switched to the corresponding output. Then I enabled in slim.conf the sessionstart_cmd  with the name of an executable script file, where the same xrandr commands are called. Worked fine on my old Thinkpad.

This would probably work, but can't try. Changed to lightdm already. Works already.

Options are usually internal (laptop), external, or both.

Edit: You could also remove the laptop screen completely if it's broken, I did this on one of mine.

Probably calling xrandr in your .xsession or .xinitrc may help.

Here my example on an older Thinkpad T410S:

xrandr --output VGA-1 --primary
xrandr --output LVDS-1 --off

But before simply call xrandr without any parameters, to figure out what the names for your outputs is. In above example VGA-1 is the external monitor and LVDS-1 the laptops own screen.

Sadly this didn't work. I want this to work on slim login screen. I assume this .xinitrc is run when login is complete, so it's useless.

If you go into the display setting, you should be able to set the external monitor to be the primary.

Bro you don't get it. I am talking about login screen... Not the display screen after the login screen.

Here my example on an older Thinkpad T410S:

xrandr --output VGA-1 --primary
xrandr --output LVDS-1 --off

But before simply call xrandr without any parameters, to figure out what the names for your outputs is. In above example VGA-1 is the external monitor and LVDS-1 the laptops own screen.