POP or IMAP? Where is the trash folder? How do you know it's not doing what you want?

With IMAP, there's no real distinction between local and "on the server" because within an account's folders, what you see in your mail client is a representation of what's on the server. So if a trash folder is created on the server, that's where the deleted messages go. And that would be the default with an IMAP account. But that won't make the messages magically vanish in your email client, becvause it shows you what's on the server.

But then you contradict yourself and say you now want them in Local Folders.

Each account has a setting for where you want deleted messages to go. Are you saying this has no effect?

IMAP

However, the trash folder at the server is empty, and I cannot recovery any deleted message