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The round connector will come apart if you remove (pull out) the red "lock" in the center of the plug.
The individual pins are held in place by a tiny clip that pushes against the side of the pins.
The trick is to pull/hold the clip away from the side of the pin while pulling the wire out the back of the plug without breaking the retaining clip.
I use a safety pin. (a big one about 2 inches per leg) If it's only one, you could replace the one pin & short length of wire & only have to make one splice.
You can use any similar size male pin & length of wire from any similar sized plug, but the color wire wouldn't match. No big deal.
If you go to a yard, I recommend getting a few similar sized/construction plugs & practicing.