Then the lender country has billions of dollars of the borrower's currency. They're either gonna spend it in the borrower country, or they're gonna sell the currency for another currency. If they simply spend it in the borrower country, that will inject the currency right back into their economy, causing inflation.

If they sell the currency, the massive surplus of that currency will cause the international value (exchange rate) of the borrower currency to fall, weakening it on the international market. That makes it harder for the importers in the borrower country to buy foreign goods, so they have to charge more domestically to make up the difference. That will cause a rippling price increase across the borrower's economy.

If your money supply was X and then you increase it to 1.5X, you can't get away from the fact that your money supply increased 50% overnight, no matter where it goes.