Proceed to solder the black cable from the AC charger to the outer wire of your Macbook connector.
Isolate that wire. You don't need to cover up the whole extension of the outer wire, just enough so that it won't touch the white cable or the circuit board of the AC adapter.
You can use the black rubber tube or electrical tape. If you use the black tube try to keep it as far away as possible when soldering to prevent it from shrinking before you cover the wire.
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