Thank you for posting.
When you perform a Copy operation in Finder, the icon should be preserved. However, the "Save a Copy As" step is effectively creating a new file. Icon data is specific to Finder so FileMaker Pro won't be able to recreate an icon.
That said, it may be possible to use an AppleScript to perform this icon assignment. There is a related example on page 63 of the AppleScript Finder Guide: