You want to use diagram "C".
1) On the aftermarket keyless entry module, ground the blue wire and the yellow wire with black stripe.
2) Connect the keyless entry module's brown wire to the OEM immobilizer's brown wire with white stripe for lock.
3) Connect the keyless entry module's yellow wire to the OEM immobilizer's brown wire with red stripe for unlock.
Do not cut the OEM immobilizer's lock and unlock wires. Just tap into them.