In 1965 the Rolling Stones played Germany, and Ulli Schröder — fifteen years old, and already a fan from the very beginning — went to all three shows. He then did what most fifteen-year-olds do, which is grow up and get a job at a bank. The difference is that the collecting never stopped. It accumulated for decades in the way these things do: records, posters, tickets, photographs, the ordinary sediment of a life spent paying attention to one band. He opened the museum in May 2011, while the building was still a construction site, and fans came from several European countries to stand in the half-finished rooms. The work was not actually finished until April 2012. Somewhere in between, the district government of Lüchow-Dannenberg looked at this and decided it was tourism, awarding him a 100,000-euro incentive.

The building had been a supermarket. That is roughly the right shape for the job — one thousand square metres of open floor, high ceilings, loading access, the architecture of bulk retail repurposed for the architecture of obsession. The museum is a member of the Museumsverbund Lüchow-Dannenberg, the local museum association, which places it in the company of regional-history collections and rural heritage sites, and makes it easily the loudest member. German newspapers have described it as the only Rolling Stones fan museum in existence, and the geography is part of the joke: this is the Wendland, a corner of Lower Saxony known for its round villages, its wetland birds and its long-running anti-nuclear protests. Not, historically, for satisfaction.

In 2012 Schröder and the artist Heino Jacobsen designed a mural forty metres long. Jacobsen then painted it onto ten garage boxes in Lüchow, working six weeks at twelve hours a day. It is not graffiti — no spray cans, no stencils, all of it applied by hand — and it depicts a train, with the major stations of the band's career strung along the line like stops on a timetable. The unveiling came in July, timed to the Rolling Stones' fiftieth anniversary. It is a peculiarly German gesture: a monument to the world's most disreputable rock band, executed with the patience and precision of a man restoring a church ceiling, on a row of garages in a town most Germans could not find on a map.

Early in 2012 the museum acquired an international reputation, briefly, for its plumbing. Schröder had installed urinals modelled on the tongue-and-lips logo John Pasche designed for the band at the start of the 1970s. Local campaigners objected that they encouraged discrimination against women. The specific complaint was a matter of design: the tongue had been left out, and without the tongue the mouths simply read as women's mouths rather than as Mick Jagger's. Town administrators said several women had complained. Schröder was unmoved, and gave the press a line worthy of the band itself — that it was neither a man's mouth nor a woman's mouth but art — before adding that the fixtures had been damned expensive and were staying. That was final.

There is no commercial logic to any of this. Lüchow is not on the way to anywhere; for forty years it sat in the dead-end pocket of West Germany pressed up against the inner German border, a place people left rather than arrived at. A museum here is not a business plan, it is a statement of intent. Which is precisely what makes the Universal Records delegation so telling: a global music corporation felt it necessary to send people to a small town in the Wendland to have a conversation about a name. Schröder gave up the name and kept everything else, including the right to hang his own face on the wall as a legal disclaimer. Few fans have ever been asked to prove their fandom quite so literally.