First remove the original connector:
Tin the 2 outer terminals of the USB plug:
Strip the outer insulation of the PSU cable back about 20mm then strip and tin the wire ends. Solder them as shown to the USB plug.
If you have a power supply with black and green wires use this photo:
If you have a power supply with red and green wires use this photo:
Finally use the 2 black plastic housing pieces to finish the plug assembly.