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Sometimes sovereign nations abandon their currencies (partially or fully) and adopt the currency of another state. For example, the currency of El Salvador was replaced by the United States dollar in 2001.
Has there ever been a case when a country with a larger economy was primarily using the currency of another country? In the above example Salvador's GDP is less than 1/500 of the American GDP.
Since Fiat money (paper banknotes) are often based on the strength of an economy of the country that issued it, it is unlikly that a bigger economy would be able to use the currency of a smaller economy due the amount of currency being printed (in circulation).
The issuing country would avoid printing to much paper money, since they are a form promissory notes that at some point must be redeemed
So in general, it is not in the (economic) interest of one country to colonize another using Fiat money, since this could lead to destabilization of their economy.
United States of America used Spanish dollar as the (sole) currency until 1792 - it even remained a legal tender until 1857.
EDIT: In 1820 (when the Spanish dollar was still a legal tender and widely used), US GDP was 12548 million dollars (in 1990 US dollars), Spain 12299 million dollars – and US grew very rapidly very soon since then, while Spain stagnated. Source: Maddison, A.: Contours of the World Economy, 1–2030 AD, Table A4.
Argentina is the classic case of a country that does not trust its own currency. Traditionally, Argentina suffers from inflation, so the US dollar is the refuge for most people. Actually, during the decade of 1990, Argentine currency was fixed to the dollar. So, during that time, Argentinians actually used their currency or dollars.
I still remember those years when Argentinians who traveled outside their country were surprised that in other countries did not accept their currency with the exchange 1 to 1 towards the dollar. They were offered far less than that.
Obviously, that fixed exchange was impossible to sustain, and ended in the crisis of 2001.
In fact, nowadays, there are four times more dollars (link in Spanish) in Argentina's economy than its own currency (pesos). The amount of dollars per capita in Argentina is the highest in the world outside the USA. The exchange is fixed by the government, but in the black market you can buy dollars (called blue dollars) by paying double. In fact, newspapers show both exchanges (check upper left corner).
So, even though Argentina still has its own currency, their own people try to not use it and buy dollars instead. But, since dollars are scarce in an economy where everyone wants dollars, the government sets a limit of dollars that each person can buy (200).
