@Legrand, look at the bottom side of the board - it might be toast (literally).
At minimum, you need to replace both the header on the board as well as the connector on the wires. If the copper traces on the back side are damaged (that includes being heavily oxidized from heat) then you can either toss the board or you can do point-to-point wiring from a suitable undamaged area of the copper traces to the header. It might be better to have the header off the pcb (hanging off the point-to-point wiring) if the board is heavily damaged from the heat.
How this happens is if there is a connection with too much contact resistance. The current flowing through the contact resistance heats the contact and eventually you get what you see. In this case it would appear that the third connector insert from the top (yellow) was causing the issue. You could have had a bad connection between the contact and the header or, more likely, the crimp was not done correctly.