Hi piotr.p,
Thank you for your reply.
I have just now written this to the one at Microsoft, that should handle my case:
Now our problem is solved.
I had written about it on two forum and a person, who is not working for Microsoft, has told me that it IS the e-mail attachments, that is the problem.
He told me that I could solve the problem for now by deleting all e-mails that has attachments in "Sent e-mails" and "E-mail outbox".
We have done that now and now everything works!
I am really surprised that Microsoft was not able to tell us that last week. And that Microsoft still has not told us, that this was a way to make our customer (and my colleagues) happy.
A big problem is solved. I strongly suggest, that you tell it to the ones working on the case.
In our case it was no problem to delete all e-mails in Business Central. Now we can test our solution on data from Production and have it ready for our customer in a few days, as planned.