"Currently it is the only living animal which has been carrying an Argos satellite beacon on its back for more than 2,628 days," Andre Fasel, curator of the museum, told AFP. The duration was recorded by the satellite firm, he added.
Max's record coincided with her arrival for autumn and winter in Morocco this week, after she left her summer nest in the southern German village of Tuefingen on September 1.
The stork was born in capitivity in Switzerland after her exhausted mother was taken under the wing of ornithologists nine years ago.
After nesting, Max eventually flew off equipped with the solar-powered beacon, allowing scientists to plot the bird's migratory habits between central Europe, Spain and north Africa.
Fasel said the project that initially involved 26 storks was aimed at identifying dangers for the migrating birds.
The scientists discovered that water towers and reservoirs in southern France were sometimes death traps, as well as power lines near Barcelona and a toxic waste dump near Seville in Spain.
"In France measures were taken to make water towers safe," Fasel said.
The bird's daily movements can be followed on the museum's website. Max spent Monday night 50 kilometres (30 miles) east of the Moroccan capital, Rabat.
Max was named prematurely after a male Swiss ornithologist, although scientists have difficulty telling the sex of newborn storks.