Transfer from external drive without duplicates?

Here's the scenario:

Mac with small internal disk was purchased.

iTunes was set up to put the library on an external disk.

Library existed on external disk.

User disconnected external disk.

User added/ripped many CD's to iTunes without the external disk connected.

New Mac with large internal disk was purchased.

Old Mac was cloned to new Mac.

User now wants to transfer all files from the external disk to new Mac (which contains all the CD's added without the external disk connected)

Is there a way to do this without ending up with a ton of duplicates in the Library on the new Mac?

FWIW, all files on the external disk do currently show in the iTunes window/library.

If I choose Add To Library and select all the files on the external drive, will it make duplicates of everything or will it just move the physical location of the files?

I have searched for answers but I've been unable to find anything related to this specific situation.

Thank you for any guidance you can offer.