You're welcome, Tangolpe

The BCX19 transistor is able to switch 500 mA.
What I mean by a pulse is for instance a signal that has been 0 V for a long time / minutes, and then changes to 5 V for a couple of seconds, followed by 0 V for a long time again. What does your PIR sensor do?
I assume that NC means Not Connected, but what does NO stand for? What is the output from the PIR sensor? A contact / relay, or perhaps a voltage?
Do you want your LED to do the exact opposite of the PIR sensor, i.e. when the sensor is ON the LED is OFF, and vice versa, no matter what?