I don't think that is true, at least not generally. In the extrem case, if 1 can produce A and B at zero costs, why would it be better if 2 produced anything as

I don't think that is true, at least not generally. In the extrem case, if 1 can produce A and B at zero costs, why would it be better if 2 produced anything assuming that the costs are non-zero for A and B? And I see no obvious reason why that would change if we go from zero to small non-zero costs. It might be true if there is an unlimited demand for at least one of the goods and we simply fully utilize the production capacities of 1 and 2 but that is not a realistic scenario in general. And even then I don't think it would be true in general. What if 2 could not satisfy the demand for B?