Stator is the same... the connector and length of wires coming out of the stator are different as Murph pointed to.
The 2013 has about 17.5" of lead from where it leaves the recoil housing to the connector end for the stator. ... I believe the 2011/12 stators had longer leads...which is good... but the connectors are different between the years.
For a clean job... IF... IF... you are good with crimping and connections and electrical in general... Get the 2011... pull your old 2013 black 8 pin connector apart... salvage the seals, connector housing and secondary lock and plug for re-use
FIRST... TAKE detailed photos and notes on both stators BEFORE you pull the connectors apart.
... and get these new pins from Mouser.
MUCH MUCH better than cutting and splicing with butt connectors or solder and heatshrink/tape.
10ea female terminals $.37 ea (8 needed, 2 extra if you screw up)
CLICK HERE
Re-assemble EXACTLY like your photos/notes show.
Pull the yellow wires connectors out of the 4 pin .250 Yazaki connector on your fried 2013 stator for re-use on the 2011 stator leads... remove the yellow wires on the 2011 connectors and replace them in the same position as you've noted and photo'd previously into the 2013 connector... making sure that the corresponding coil wires go to the corresponding cavity on the plug. The terminals inside the 2011 are the same as the 2013.... (90% sure)... and will click back into the 2013 connector that you are re-using.
Plug it in... and go... probably about 20 min worth of work for a plug/play result.
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