Mike... bad news, me again..
You wrote "so to replace that section please go into detail "
This repair to your (green / earth) wire within the loom. Basically you'll need:
(1) A replacement length of wire, MINIMUM 15A rating. Try shopping here, look in the menu 'Cable', and within here either Standard... OR Thin Walled Cable. The latter is more modern, with an abrasion resistant sleeving, but a little less pliable than the Standard cable. Read the intro blurb for each, and make your mind up. (think I'd go standard). Then choose a wire that is greater than 15A capability. Then choose Green (!) and the length you want.
http://www.autoelectricsupplies.co.uk/category/10I think you can also get 15A automotive wire from Halfords... and maybe Maplins.
(2) You'll need to insulate the joints you'll be making, and I'd recommend you use HEAT SHRINK TUBING. Go to the same link above, and within 'Sleeving' menu find 'Heat Shrink Sleeving'. Choose the colour, diameter and length. (This diameter will approx halve when heated, don't forget, it'll initially have to fit over your 'bulky' (ish) soldered joint. Ie don't skimp on the diameter)
(you can also get heat shrink tubing from Maplins)
(3) You'll need a 40W soldering iron + solder..... Maplins / Halfords, < £15 or so
(4) Wire strippers.... Maplins / Halfords, £5 tops.
(5) Black insulation tape to bind the loom back together @ the end of the repair.
What you do...
Cut back the existing loom external / main black insulation up & down the abraided earth wire until you get a couple of inches of 'Virgin' green wire each end. Cut out the bad bit. (do NOT plan a joint where the loom takes a turn etc - ie choose a straight run)
Strip back about 1cm of insulation on each end, and ensure the copper wire is CLEAN.
Cut a length of your new green wire to splice in, and (again) strip about 1cm of insulation off each end.
'Tin' each of the 4 bare wires individually .. ie heat them with the soldering iron & apply solder.
(if you're not comfortable with soldering try a few joints away from the bike & on the bench until you get happy)
Join one end of your new wire to the existing loom, lay the tinned ends side-by-side and heat with the iron. Apply more solder if you have to.
Cut 2 pieces of your heat insulation tubing, about 3cms each, & slide over new repair wire splice. Move it well up the new splice, ie well away from the heat of your next solder joint.
Solder the second joint. (these joints must look shiny silver on completion, not dull)
If there are any 'sharp' points about your joint send the missus to the shops & nick her nail file to 'make it all better'
Slide each piece of heat shrink tubing over each solder joint & heat with a hair dryer until it shrinks tightly over your repairs. (you can use a match / naked dull flame... but get the tank well away!) (Again, if new to heat shrink tubing play with a few test bits until you've got the hang of it.)
Bind the whole repair area / loom back up with the black insulation tape. Take care with the ultimate routing... you were LUCKY you abraided the earth wire, chances of that happening versus the others!
Pour yourself a beer...
Enjoy!