First you need to clean up that line of text. 'Retention' and 'future reference' sound pompous. Just tell them you are enclosing the copy. Let them decide what to do with it.
Then yes, you need Enclosure: or Encl: at the bottom, too.
A 'duplicate original' I would take to mean that it is one of 2 identical original documents (i.e. both signed in ink or sealed, for instance). This is different from a copy of an original (i.e. photocopied, scanned, etc from an original document.).
Now that I re-read your first post, you seem to be enclosing a copy of the very letter you are writing! That is a very odd thing to do. Is
It is a engagement letter written to a client that provides a signature line for them to assign to show agreement with the terms outlined in the letter. I want to provide a signed copy for the client to keep and I want one returned to me. I have mentioned providing this additional copy in the letter, and I wasn't sure if it needed to be identified in an "Enclosure" line at the end caption below