Hi,
Thank you so much for taking time to solve our problem. The incompatibility of the machine with online services is probably the reason for our troubles.
The email address that was set and worked until recently was kettnercom@1und1.de, the server was smtp.1&1.de (we are located in Germany, 1&1 is one of the leading providers of mobile and internet services). It may well be that the servers of this company got an update and our machine no longer meets their requirements.
The other email addresses we tried to set were from mail.com, gmx.com and strato.de (another major provider of mobile and internet services in Germany), all of them showed the same problem - most likely because of what you said.
So how can we set a relay on our machine? Which email addresses could be suitable? We are happy to get a paid email address if we have to.