I've read somewhere that this might have to do with the fact that after WWII, the Axis powers were forced to demilitarize and thus put all the factories and workers who used to produce war materials to work on other products like fountain pens, musical instruments etc. Is there something to this theory?

This doesn't hold up to closer scrutinity though it sounds pretty good as an explanation when first reading it. Problem number one with this theory is that the demilitarization of industry is not a phenomenon exclusive to the Axis powers. Even with the Cold War looming on the horizon and the rise of the industrial-military complex in the US, the Allied powers too had to transition from a war economy that had mobilized the vast majority of all industrial resources of a country, especially in the US, in service of the war into a peace time economy. By 1944 about 37% of the GDP of the US was defense spending, which amounted to more than 80% of the money spend by the federal government that year. Translated into actual production that is enormous. And once the war was over, numbers went down: By 1950 defense spending amount to 5% of the GDP and 32% of federal spending. This can directl be translated into less ships and ammunition and aircrafts build (in percentage of total production capacity) and more factories builidng cars, fridges, radios and other consumer goods.

Another problem with this theory is that at least in the German case, production capacity in terms of avialable work force changed drastically after WWII. Not only was Germany divided between the two occupation zones to grow into FGR and GDR but also the workforce changes massively overall: By the end of 1943 and early 1944 over 25% of the total workforce of the German Reich was foreign forced laborers and concentration camp prisoners. What kept the German war industry running so long was the massively violent and brutal system of forced labor. This was for obvious reason not sustainable after the war and thus war production capacity can't be translated 1:1 from in to after the war. However, one factor here could be that on average, companies not as essential to the war as others tended to receive less foreign laborers than others. Pelikan for example did explicitly use forced labor camps and concentration camp labor in their production during the war which was centered around military paints and chemicals. But in their fountain pen segment there was probably a greter degree of continuity of worl force for whatever work force was spared from going to the front.

Furthermore, at least in the German case, a lot of the companies that produces massively for the war, simply returned to what they had produced before the war. Porsche stopped building tanks and Kübelwagen and went back to building cars. Mercedes also went back to cars and simply painted their Wehrmacht lorries different. Messerschmidt was not allowed to build airplanes so they retooled and build engines and other things that were used in aiurplanes but also elsewhere. I am not a 100% on this but the only company that went into fountain pens is Porsche but I think that might be more related to them trying to sell what they conceive as luxury goods in general and happened later.

And I think the reason for the prevlanece of fountain pens from Germany after the war up until today is to be found here: Germany at least – and I would assume that holds true for the other two countries as well though there I am less sure – had a famous fountain pen industry before the war. Pelikan, Montblanc, and Kaweco are all companies founded in the 19th or early 20th century that had been established and successful by the time of the Post War. Some of them are even known for relatively important innovations in the field of fountain pens.

The histories of these companies is a history of German industrialization. Fountain pens sit at an intersection of two manufacturing branches that were highly successful, incentivized, and promoted in Germany: The manufacture of comparative complex technical prodcuts and the chemical industry. One factor that predicated the rise of these industries and that Germany shares with Italy and Japan is an industrialization that came without a colonial empire. Germany, Italy, Japan were comparative latecomers to the club of European imperial powers with large colonies in Africa and Asia. Germany's colonial ambitons began in the 1880 – by that time Germany was industrialized. Without a colonial to provide cheap and readily available resources for industrial manufacturing it is not surprising that f.ex. cotton manufacturing didn't take off in Germany. Instead investment policy followed things that could be done there directly, including such things as the chemical industry, which also needed reosurces but not on a manufacturing scale of cotton weaving and by then things like rare earth and such were still common in small quantities needed in Germany f.ex. That's how you get to BASF and IG Farben as the largest and most successful chemical manufacturers world-wide until 1945. And a solid industry that helps devleop chemicals helps the fountian pen industry.

In short, the prevalence of fountain pen manufacturing in the former Axis countries is more likely related to the peculiar histories of their industralizatin, which predates their cooperation in the Axis though this shared history is certainly not the only factor in all of that. However, the idea that re-industrialization resulted in the rise of peace industry does not really hold water.