Sorry, corrected the quote
Just to clarify: phpBB founder / administrator or any other user from the phpBB user management are not involved in this process.
It is the php / web server user which is operating on the files inside phpBB.
Is this user different from the ftp-user?
Can you delete other folders from the file system with the ftp user?
Has your ftp client program any information about the owner / group of the folder?
And maybe ask the host, why the ftp user is not allowed to delete a folder from his "own" file system.