I understand from this answer (near the end) that whether factor scores will reproduce interfactor correlations depends on the method of factor score estimation, and thus that it is not in general true that factor scores will reproduce interfactor correlations.
This comment suggests that a relevant formula is embedded in certain other answers, but I had a bit of trouble recognizing the formula, and thought the issue was important enough to warrant a separate question.
This answer gives code for how it is calculated in one particular package in R, but not the formula.
Ideally a response to this question would give not only the formula but some intuition for why it is appropriate for interfactor correlations to be calculated in this way, and also cover the question of whether there is one canonical formula or a variety of formulae that are more or less justifiable.
