The three phase wires
(Motor A, B and C) and the five hall sensor wires
(Motor hall) will obviously need to be connected to the motor in place of the old controller.
The "Power +" connects to the battery + and the "Power -" connects to the battery -.
The "Power switch" connection will need to connect to the Battery +
(either directly or via a separate on/off switch).
I'm guessing that the "Turn the lpug" connector is for the throttle
(or a voltage mode PAS sensor).
I'm also guessing that the High line and Low line are for different styles of brake switch. GM uses a Low level signal
(connects the blue signal wire to the black ground/0V) when the brake switch is activated to trigger motor cut out function.
Other scooters with a 12V lighting system often use a 12V High level signal
(which also supplies the brake light bulb while braking).
The "Instrument plug" should not need to be connected.
You shouldn't need the "Burglary power" or the "Signal theft" wires unless you particularly want to incorporate an anti theft function, which presumably requires a horn to be fitted also.
The "Reversing Plug" wires are only required if you need the reverse function.
The "Three-speed plug" is often connected to a three position switch to allow different power setting to be selected, but it should work without this at one fixed level , but I'm not sure if it will be high, med or low though .
I'm not really sure what the "Learning plug" wires are for, perhaps they are used for setting the Phase angle to suit the motor?
It might be worth asking over on the
Endless-Sphere forum as I expect someone there may have experience with that type of controller.
Alan