Archive is a separate folder. Actions performed on other folders such as Inbox and the local folder won't affect the Archive folder.

My question would be to ask how and why there is a copy in Archive in the first place.

Exactly I have no idea how there is a copy in the archive folder. When I receive a mail, the message is present also in the archive folder, but deleting it from the inbox remove also from the archive (and vice-versa). This is a behavior that i would avoid, anyway using the message filter leave a copy in the archive.

Is this an account that uses IMAP? Might this "Archive" folder be a "feature" of the email service?

Thunderbird's own Archive folders have an icon with, typically, a folder with a blue strap around it. If yours isn't a genuine Thunderbird Archives folder, I'd expect it to have a regular folder icon. And that would suggest that an external agent is responsible for populating it.

Yes, I use only gmail accounts (IMAP). The archive is not a feature of the email service but seams to be related to some "strange" operation of Thunderbird.

Ah. Gmail.

Gmail has the unusual "All Mail" folder where they actually keep everything, but manage its contents using labels. "All Mail" also stands in for Archives (the archive settings are partially disabled in googlemail accounts, for this reason).

I don't, myself, see any reason for displaying All Mail in Thunderbird. Everything you want to see should be shown in its proper folder (Inbox, Sent, Trash etc) and showing All Mail simply duplicates this. If I have deleted something, then I don't need or want All Mail to be constantly reminding me that it's still there but ordinarily hidden.

Basically, whatever you have in any of the account's folders should also appear in All Mail, so in the case of All Mail, it's no surprise that moving messages from folder to folder has no effect on All Mail. After all, that's where it is stored; only the labels change.

Now, is it possible that your "Archive" folder is actually "All Mail" in disguise?

Googles idea of archive and your and mine are very different.

Google think you never ever want to get a mail off their server. So when your delete a mail it leaves a copy in the All mail folder (The archive)

Go here https://mail.google.com/mail/u/0/#settings/fwdandpop Change what happens when you delete a message (Move is a delete by implication, the IMAP server knows nothing of the new location so can not move the mail.)