by Ahmad ElGazzaz.
Thank you for the invaluable information.
One of the first things I tried to do is to upload a file and find it in the moodledata folder. I did find the file but it was tiresome.
Back to my problem, I can not find any errors in the log related to the inability of writing in the moodledata folder. I tried to follow the instructions on the moodle documentation for moodledata folder permissions, but the website was inaccessible so I restored the original permissions.
EDIT: I noticed when I tried to backup a single course I get to the import screen with all the backups of this course in the automated backup section