When physical money is sent out of the country, it shrinks the supply of digital money in fractional-reserve American banks, making prices cheaper. Inflation is exported mainly by illegal immigrants.
On the other hand,
Bank-created inflation is not exported. It stays in the trade zone of the nation that creates the money. In today's floating exchange rate system, price inflation in the United States does not affect the price level (a statistical index) in any other country for very long or for very much. Bank-created inflation is not exported. It is merely copied. When foreign prices rise alongside America's rising prices, this is because foreign central banks are matching the monetary policies of the Federal Reserve. Domestic digital inflation is always a domestic bank–inflicted wound. Central banks compete with each other to debauch their domestic currencies. This is not free market competition. It is competitive plunder by government-licensed counterfeiters.