I did contact my non-Apple mail provider. This is also something Apple asks you to do. As I have already written, I have two e-mail accounts with the same provider. But the second one (which has the same configuration, apart of course the name and the password) has no problem! This is the most weird part of the issue.
It is for sure a problem of the app. In the « advanced settings » of the incoming server: at the top you have the possibility to set the folders of the mails. Well, with my problematic account I do not have the possibility to choose the folder of the sent emails. The only possible choice is… my Phone!!!
There is another very strange thing. We can all send e-mails from these problematic accounts; but where are these sent emails stored??? I cannot find them! They are nowhere.
Anyway. Now I have both Outlook and Spark installed and of course not the ‘Insecurity Mail’ as I cannot carry my laptop in the forest.
Next update: next Tuesday (Unless I have something to report before)