Has any state ever performed an "economic attack" against another state, by printing fake money of the victim's currency?
Or, is it known if someone ever considered doing it, and which were the supposed pros and cons?
Frederick II the Great, king IN Prussia 1740–1786 used to counterfeit currency of the Polish-Lithuanian Commonwealth (PLC) on a large scale, for profit and to economically weaken Polish state. Officially PLC wasn't at war with Prussia but the only reason that this and other hostile activities of Frederick the Great were unanswered by PLC was the weakness of Polish administration at that time. (and that's probably the reason why he did it).
Frederick obtained the dies for Polish coins during his raid on Saxony during the Seven Years' War (1756-1763). They were there because at that time PLC was in a personal union with Saxony.
EDIT: Wikipedia piece about this particular episode of Frederick's activity points to those books in English as sources: Hamish M. Scott, The emergence of the Eastern powers 1756–1775 and Norman Davies, Europe: A History
The US government alleges that this has occurred - see Superdollars. Very high quality counterfeit $100 bills flooded the US market. Although it may be that these were merely a way that the responsible institution was funding operations, it is commonly believed that these were also intended to cause inflation within the US by increasing the money supply. I don't see any information about the total value of the counterfeitted currency, or how that relates to MB or M1. One would need to have that value in order to have any hope of estimating the inflationary impact. (and one would have to resolve certain controversies between classical and liberal economics).
That article also references Operation Bernhard, which I think @DVK mentioned.
During World War 2, Germany carried out Operation Bernhard-- one of the biggest currency counterfeit attempt in history-- to destabilize the economy of Britain and the United States.
The operation was named after (and started by) NSDAP member and SS Major Bernhard Krüger, who led the operation from a segregated factory built at Sachsenhausen concentration camp, manned by 142 Jewish inmates.
The operation was started initially to forge the Bank of England pound notes in denominations of £5, £10, £20 and £50.
By 1945, the production had successfully reached 8,965,080 banknotes with a total value of £134,610,810.
Interestingly, after the war, a part of this counterfeit currency fell into the hands of the Jewish underground, who used it to bring displaced persons back to Israel.
During the American Civil War, the Union attacked the Confederacy in this fashion. While this was work of a private Union citizen; the work was tacitly permitted by the government.
Considering the technological advantage the North had over the South; they could have industrialised this strand of economic warfare with great ease. They only refrained from (formally) doing so because it could have set a bad precedent for counterfeiting after the war. Indeed, the original purpose of the Secret Service was to protect against this very risk - what with the lowering cost of printing presses and supplies.
At least 1 - 3% of all Confederate money was fake and it causes a problem for collectors to this day.
During the French Revolution, European powers (and displaced French aristocrats, known as emigrants ) opposed to the Revolution flooded France with counterfeit 'assignats' - paper currency, in an attempt to undermine the French economy after they had disposed of Louis XVI.
Thomas Carlye: The French Revolution, a History Chapter 2.5.II: (One of several references there.)
Also they (agents of the Kaiser of Austria) have manufactories of False Assignats; and men that circulate in the interior distributing and disbursing the same; one of these we denounce now to Legislative Patriotism: ‘A man Lebrun by name; about thirty years of age, withblonde hair and in quantity; has,’ only for the time being surely, ‘a black-eye, oeil poche; goes in a wiski with a black horse,’(Moniteur, Seance du 2 Novembre 1791 (Hist. Parl. xii. 212).)—always keeping his Gig!
In present time, Pakistan is waging a proxy war with India, which includes destablising the Indian economy by printing large sums of fake currency. Just search Google with 'Pakistan Face currency Racket' and you will be presented with both reputable and not so reputable links.
After a massive loss of people and land in 1971 Bangladesh Liberation War, and nuclear tests by India in subsequent years, the balance of power shifted in India's favor. Since Pakistan now cannot sustain a full fledged war with India, its ISI (intelligence agency) was tasked to create a road map to take revenge. To destablise its arch-rival India, Pakistan started to use unconventional methods. The first one was to use terrirism. But you need the money to support it and since Pakistan was already short on money, ISI invented a novel way to print fake Indian currency. It makes money by producing and selling counterfeit currency, and in the process, it harms the Indian economy and fund terror groups as part of its mad terror and proxy war against India.
It may be recalled that a few years back, a First Secretary of the Pakistani Embassy in Kathmandu was sent back to his country because of his clear-cut involvement in sending the counterfeit currency to India.
According to intelligence reports, initially the fake Indian currency was printed in only one or two Pakistan government presses. However, as ISI has been able to successfully enlarge its network in Nepal, Bangladesh, Sri Lanka, Dubai (UAE) and even in India itself with the connivance of gangsters like Dawood Ibrahim, the fake Indian currency is now being printed at several government-controlled presses in Karachi, Multan, Quetta, Lahore and Peshawar.
There are unconfirmed allegations that ISI has also been able to print some fake Indian currency in Bangladesh under its direct supervision.
The Pakistan government imports the special paper and ink from UK, Sweden and Switzerland. As the material is much more than its own legitimate requirements, the excess bulk is diverted to ISI, which is regarded more as an international terror and sabotage outfit now than an ordinary security agency.
So the answer is yes, fake currency has been used before (by Germany in WW2) and is being used in current period as I have stated above.
In the post-WW2 (1945-48) occupied Germany, the currency was Reichsmark, printed by both Soviet and Western administrations in agreed-upon amounts. The Soviet administration ignored the agreements and flooded Germany with Reichsmarks, causing the rampant inflation which forced the Currency reform of June 1948.
The goals of the Soviets were manifold, and the inflation was not necessarily the main one.
This was the time when both victorious sides were scouting Germany for technology, especially rocket, and pay generously was an important way to prevent the engineers and scientists from defecting to the West (this is described in Boris Chertok's memoirs).
This probably does not qualify as an precise example asked by the OP, but, IMO, it is a relevant episode.