Perry is right about the star wheel on the self-adjuster needing to be fixed to the rear shoe. It follows that the self adjusting arm also must be pivoted on the secondary (rear) shoe - so it can make contact with the star. Those locations/positions are fundamental to how these self adjusters work. This self-adjusting action happens when the brakes are applied - but only when the vehicle is moving in reverse.
When you are backing up and apply the brakes the rear shoe is pulled downward, thus levering the adjuster up on the star. If the adjusting arm is mounted to the front shoe, when the brakes are applied while backing up, the opposite will happen. The front shoe will move upward and cause the arm to move down in relation to the star wheel. This won't cause the brakes to un-adjust themselves, but they won't ever move from the point where you left them. As the linings wear, the clearance will just keep getting bigger and bigger - a loss of braking performance will eventually develop.
I suppose a case could be made that; with the arm and star wheel being operated by the front shoe the opposite would apply. The self adjusting action would then take place each time the brakes are applied while moving in the forward direction.
Here are a couple of images.
First one shows the brake components layed out in their proper locations:
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This shows (and clearly states) that the adjusting arm should be pivoted on the rear shoe - and also that the star wheel end of the self-adjuster should be closest to the rear shoe:
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Finally, an image showing what the brake components should look like when everything is fully assembled:
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