Backlight of the display isnt working, can I test a 13" display?

I’m sorry you received a wrong answer and hope you haven’t burned out your friend’s screen too. Retina screens don’t have any inverter, as a matter of fact neither the previous generation used inverter based technology that was last abandoned by Apple with the latest A1181 manufactured in 2009.

Even when connectors look the same, they might have a completely different pinout and suggesting to test freely different size screens without a previous pinout check I find it pretty asinine.

Try to put back in place the A1502 screen to the 13” to make sure it’s still working, if not either it got burned by a different pinout setting or by a possible short present on the 15” backlight circuit, but cross my fingers.

As far as your backlight is concerned, you’ll likely need the help of a real technician who could do some basic testing before plugging in a screen worth several hundreds to “see if it works”