Good luck with a S3 service manual, there has never been a hint of one for the M3W. Most of the servicing and maintenance information for the M3W has come via this forum, mainly learned the hard way by owners. I don't think the dealers got any detailed information either.
If you want to align the rear wheel straight with the body then there is a procedure that is detailed on the MTWC website 5 Speeder section. Assuming you don't have access to that it is essentially laying a laser level along the rear wheel sidewall rim and point it at a target positioned centrally between the front wheels and offset half the rear wheel rim width, plus the laser offset. On the M3W I use the number plate mounting screws to fix the target and mark the rear face, not an option on the S3. This will allow you to accurately align the rear wheel, you also have to juggle the drive belt tension and hope it doesn't all move as you clamp up the axle nut. Some trial and error involved to get it all perfect and the belt tracking well. Once you have a good tracking belt then you can mark the target point and reproduce the "good track" position easily after tyre changes etc.
A steel straight edge along the side of the bevel box drive sprocket and rear wheel sprocket helps a lot with alignment of the drive belt as well. You may need to adjust the rear swing arm pivot mount bolts to get this in alignment. The guide plates should be just that guides, not restraints. If the belt runs up hard against front or rear sprocket guide plates then eventually they will fracture.
