Method
Only do this if you are confident with electrics and that you can achieve it safely, only for 5 Volts USB supplies.
Check all wiring and voltages, etc..
Use a USB extension cable, (a short one will quite often do).
Cut the USB extension cable in half, then you have a USB socket with a cable and a USB plug with a cable.
If the Power supply unit normally goes directly to the camera cut this USB power cable at a suitable place, allow for wire movements', etc..
Use the USB socket from the cut USB extension cable to join to the Power Supply Unit. Use insulation for example heat shrink tubing connect correct wires.
Now you have the power supply with a USB socket fitted. This may be used as a power supply to plug in any suitable USB unit.
Join the cut USB extension cable plug to the power cable odd shaped, (proprietary), that is the camera, (in this case, but could be for anything). Use insulation for example heat shrink tubing connect correct wires.
This USB Plug, that is now connected to the cable that went in to the camera odd shaped, (proprietary), may be plugged this hacked USB socket that is now on the power supply unit. I use this for longer Camcorder time by plugging into a USB battery pack.
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