"Ok... so the outside company will spend $9m buying Iraqi raw materials etc in order to produce shoes, and then sell them for $5m."

No. Remember how the "outside" company is twice as efficient? That means it makes twice as many shoes (of the same quality) out of $9m raw materials as the Iraqi company. So it will still sell the products of those raw materials for $10 million, but the difference is, it will sell twice as many shoes.

That means Iraqis who were going to pay $x for one pair of shoes can now get two pairs of shoes with $x, and Iraqis who previously couldn't afford shoes, now can afford a pair.