No subject

  \Recent   Message is "recently" arrived in this mailbox.
    	    [...]
	    This flag can not be altered by the client.

Anyway, when a message is copied/moved to another mailbox/folder, it
should have the \Recent flag set because it just arrived in the
(target) mailbox, and mozilla should see it as recent.  Is the mailbox,
where the messages were copied/moved, re-opened after the copy/move?
Then you shouldn't define the target mailboxes in the account entry
with the "folder" keyword, because then imapfilter checks them and
the \Recent flags are unset.