Word file links are always absolute. Moving the files to another computer is OK provided that computer has exactly the same folder path to the source files. Given the absolute nature of the links, though, that also means you can move the Word file about without breaking them.
To see how to implement relative paths in Word, check out the field coding and macro solutions I've posted in the
Word Fields and Relative Paths to External Files 'Sticky' thread at the top of this forum:
https://www.msofficeforums.com/word/...nal-files.html
Note: Since links to Excel files employ LINK fields, you'll need the macro solution.