I uploaded the Leaflet map to Github now. Thank you to @Roboe for kickstarting the Github adventure and helping me with the first steps! 
You can find the repository here: https://github.com/WeAreFairphone/fprsmap
I warmly invite you to contribute!
PS.: In order to keep everything connected to the forum, I’d say that people can only add their Fairphoners community to the map after adding it to the Local Fairphoners Address Book, providing a link to that address book entry.