I think a first-order explanation (that probably breaks down quickly) is that often many fixed costs are paid in the local currency, such as salaries and rent.

I think a first-order explanation (that probably breaks down quickly) is that often many fixed costs are paid in the local currency, such as salaries and rent. To be profitable (in the local currency that they care about) they need to take a certain price, otherwise they're operating at a loss. Currency fluctuations affect all these factors equally so that in the end your product is cheaper for the importer. The salaries and other costs are of course lower as well when the local currency is exchanged to whatever currency the trade is taking place in. The flip side is of course when you rely on imports to produce your exports (natural resources for example)