If you remove the brown connector from your old stator before removing it from the bike, then fasten a bit of spare cable or rope to it and pull it through. Then, when you fit the new stator fasten the cable / pull cord to your new stator lead and pull it back through.
The cable route from the stator goes straight up to the inside of the left frame beem , over the wiring loom and down through the V of the motor, behind the coolant tank to the rectifier.
Some bikes have a cable tie holding the stator cable to the loom (left side of the bike just below the tank) if the cable is tight then you need to remove that tie. Easy to get at if you lift the fuel tank into the service position.
Athena gasket for £10 off eBay.
As for putting the stator cover back on, It's easier to get 4 long bolts (or threaded rod) cut the heads off and screw them into the engine - they act as a guide for the cover to slide in place without being pulled by the magnet. Also helps keep the gasket in place....
Just in the process of doing mine..... again !
Original lasted 21k, Ricks replacement lasted 12k...