What happens to the currency of an invaded country?

i think the currency is allowed to to continue, unless of course the invading country completely takes over and establishes an empire in the name of bringing democracy

Regarding currency (and ignoring investment completely), this depends on the situation.

In cases of metallic currency, i.e. gold, there's no problem as it can be converted at any time.

However, with fiduciary currency, the situation is different. The value might decrease since the issuing country's government is no longer solvent and any foreign exchange pegs, etc., will fail immediately. The value might increase, thanks to massive increases in demand for cash that correspond to emigration and displacement usually found in invasions.

As for a practical example: in the case of Iraq a few years ago, the fiduciary currency of the country significantly increased overall due to latter of the above as well as the fact that with the previous government's central bank dissolved, the high inflation historically common completely abated. This actually increased the demand for the currency as its supply had previously fluctuated so much that the new stability and availability of the currency allowed it to be a more efficient method of exchange than during the previous regime. (Note: this was the opposite of many economists' expectations, and the interim authorities had difficulties working with this phenomenon at first.)

Depends on invading country really.

Cash currency and bank accounts will probably remain or be exchanged into currency of invader. You'd get major riots if you just wipe out savings of everybody in the country.

Investment and property might get expropriated.