What is the ruling on the financial increase resulting from the difference in exchange rates between a foreign currency and a local one when sacrificing on behalf of another, and is it due to the one sacrificing or to the one on whose behalf the sacrifice is made?

It is permissible to appoint an agent to purchase the sacrificial animal without first giving the agent the money. This is considered a loan from the agent. The loan must be repaid in the same currency, or in another currency at the exchange rate of the day of repayment, not the day of purchase. If you did not keep the dollars for yourself but exchanged them, then you should only take the equivalent of what you paid in local currency, and return the excess to your principals, for an agent does not profit except with the permission of his principal.