My wife was not able to do it, but I found a solution, so I want to share how to use a recording as ringtone.
In the Recorder app we recorded a nice ringtone. However in that app we can only rename the recording, but do not get the file.
However to get the file, I used the apps share feature. And I shared the recording with Google Drive.
From there I can download the ringtone file.
Back on the phone I used the files app to move the file from downloads to the ringtones directory.
Finally, in the settings I was able to chose the new ringtone. And now I have my daughter calling me when I have a phone call: