We've actually managed to do it. But we needed a little 3rd party help in the end. But I'll come to that.
First I followed this comprehensive guide:
https://steamcommunity.com/sharedfiles/filedetails/?id=514493377 This looked very good and I launched a server on my computer. But my friend was still unable to connect. Further analysis indicated that the default ports for Zomboid seemed to be still unreachable for my friend (we used
https://www.yougetsignal.com/tools/open-ports/). That was odd because all port forwarding settings on my router looked okay.
Then I stumbled over an article that suggested, that my internet provider had to change a setting for my connection to allow port forwarding. But the nice lady at the hotline told me that they are not blocking any ports.
Frustrated, I mused over the problem for a few days. Then I remembered a tool I used years ago to play a different game online: Hamachi. It creates a VPN peer-to-peer connection between computers over the internet so for the computers it looks like they are in the same network. Using Hamachi is dead simple and there are some nicely written guides available online so I won't get into details here. [edit] Just one thing: When you want join a server you have to type in the Hamachi-Ip-address displayed in the Hamachi window for the hosting computer into your Zomboid server-join dialogue. If you have any questions just ask here. [/edit]
In conclusion that software was the key to our success in the end.