Not sure from your images, but it looks as if the brown wire is just looping through from L1 to L2, which would be correct, if that is the case.
It would be easier if I could do a drawing and the post the image, but my computer skills are very limited, and not up to posting images, so I will try to explain three phase starter wiring for single phase.
At the feed end of the starter you have L1, L2, L3, there may not numbers on your starter, but if you count from the left (looking at the starter).
Connect the single phase live to L1, input to starter, at the output end of the starter connect your loop wire to L1, output, the other end of the loop wire goes to L2, input, your live output will now be at L2 output. The neutral in and out will be through L3. The motor is then feed from (L2 live) and (L3 neutral).
Important, the above is the normal way of wiring three to single phase starters, but it depends where the contactor coil and hold on contact is wired ?.
Hope this helps.
Chris R.