Wire had just parted company Edoh so resoldered it but I'm sure its obtainable at reasonable cost. You could probably use 200amp battery cable at a push but that cable twists and turns a fair bit from one end to the other- hence the reason they used braid.
Had to use a gas-powered soldering iron (ALDI special) with the nozzles removed to get the heat needed. A domestic electric one is no good. I found the best way was to solder the braid, solder the body on its own then put both together and apply enough heat to melt the solder until they fused.
If you do get a completely dead starter (ie not even a click) and neither solenoid or motor will work on their own, then that wire will have come adrift. Its the crucial path for both. Sometimes they rot away altogether but making a judgement on whether to replace it or not will depend on condition of starter as a whole.
If motor works but solenoid doesn't, you'll have to fit a new solenoid but you'll really struggle without a vice and impact driver as the screws that hold it on are a pig to get out and will chew out easily. New solenoid about £20 I think depending where you buy.
I keep meaning to do a video on brush replacement. Will do that over the Summer as my old starter motor just needs those to be put back into service and they're only £7 for a set.
Far too many starters get swapped out (at £150 - £300 a go) when the fault is just dirt, brushes, solenoid or a connection issue. I can see why people buy recons rather than mess but replacements are incredibly overpriced. If you're on a tight budget, finding and fixing the fault has to be worth a go. If it doesn't work, screw it back together and get another.
