What IMAP server are you using?
Have you set in it to propagate permissions from top level to sub folders?
How are the permissions for the folders that do not work for this user?

"What IMAP server are you using?"
We are using iRedMail.

"Have you set in it to propagate permissions from top level to sub folders?"
Yes every folder has a full Permission and it is working with Outlook or with the SOGo Webinterface

"How are the permissions for the folders that do not work for this user?"
Our Example is a Folder called Backup

My User has the Permissions:

• Read mails from this folder
• Mark mails read and unread
• Modify the flags of the mails in this folder
• Insert, copy and move mails into this folder
• Erase mails from this folder

What else I can say is that reading of mails works well. But deleting or moving them in a other folder will not work with the Thunderbird client. With the SOGo Webinterface it will work and with Outlook Client also.

Then you use dovecot as IMAP server.

Does the user have privilege "Post mails" for the target folder?

Yes the User has the privilege on the target folder. But still not working.

I usually have set privilege "Expunge this folder" on shared folders with erase privilege set. But this should not affect moving/deletion.

Strange thing is that right now moving a Email from our Folder called Backup is now working. We didnt changed something or restarted the Server. Very strange. Trying now on a other Folder and it won't work from this.

If I grant the user full access dont work either.

This is a general Thunderbird question.

I created a Bug Ticket at Mozilla with this Issue. A People said that this Issue appears only for Thunderbird because the "e" permission is missing. I also checked that with connection via openssl to our dovecot server and typing this command:
a setacl Junk <myEmail> +e
a setacl Trash <myEmail> +e

After adding the permission "e" the move from folder Junk to Trash works. It seems that SOGo is not adding the "e" permission correctly when I give a user full access.

Mozilla Ticket: https://bugzilla.mozilla.org/show_bug.cgi?id=1595730

And this is not a TB questions because Outlook is not using the "e" permission. Outlook copy the mail from Junk to Trash and mark the mail in Junk as \deleted.

This is why Outlook can move the mails without issues.