Unfortunately, there is no easy way to get the new uniqueID (Rebex ID) of a copied message. The IMAP protocol's COPY command doesn't return this information, unfortunately.
But the following approach usually works fine and is simple enough:
' get the "next unique ID" of the target folder
Dim nextUniqueId As String = imap.GetFolderInfo("Other").NextUniqueId
' select the Inbox folder and copy a set of messages to Other folder
imap.SelectFolder("Inbox")
imap.CopyMessage(messageSet, "Other")
' select the Other folder and search for all messages whose unique ID is equal to "next unique ID" or larger
imap.SelectFolder("Other")
Dim newSet As New ImapMessageSet
newSet.AddRange(nextUniqueId, ImapMessageSet.BuildUniqueId(imap.CurrentFolder.ValidityId, UInt32.MaxValue))
ImapMessageCollection list = imap.Search(ImapListFields.UniqueId, ImapSearchParameter.MessageSet(newSet))
' now, the list should contain info about the copy message including its unique ID
(You might also speed things up a bit more (depending on the server) by selecting folders in read-only mode (see SelectFolder's second argument).)