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Best first look for a schematic or similar online resource to see how many wires it holds and their mm2, and if possible, how the controller fits together if you intend to take it apart to completely replace the cable.
You might be able to cut it off about 20 cm from each end and replace it with ethernet cable or similar and solder the wires together with heatshrink tubing to prevent shorts, unless you fancy taking the controller apart and won't find it impossible/a lengthy and fiddly procedure to fit back together (e.g. button covers are usually a nuisance to fit back in the right place).
'Recover' as in only replace sheath, waste of time imo as wires may be cooked hard, too.
Since the wire is black colored, you can cover the damaged section with liquid electrical tape, and depanding on the size of the connector, try covering the repaired section with a small lengh of heat shrink tube just to give some robustness.
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BTW, I wonder why did you attached a picture with so much stuffs in background when could show only the defected part of the cable: