Old issue, but I can add a layer that hopefully helps...
MS Word will make an inline (text only) caption when the graphic is set to inline. If the graphic is set to wrapped, it will put the caption in a text box. The text box version of the caption defaults to an absolute link (http://www.yoursite.com/yourdoc.docx, or c:/folder/yourdoc.docx). The main issue with the absolute link, like the OP mentioned, is that when the document is moved or exported, the absolute links point to a reference that will not be available and makes the document unusable. Captions made of inline graphics, appear as text only, without the text box, and are a relative link, so the link only points to within the current document.
Solutions.
- First Work around is to delete the offending caption, then select "In line with Text" for the wrapping option, then re-make the caption.
- A second, more technical solution, that maintains the formatting of the document in the captions, is to mouse over the individual entries for the list of figures. Items that show a URL when you hover over each entry, are usually tied to a text box. Right-click the entries that show a URL on the mouseover and select toggle field codes. When you see the field code, A code will appear with a hyperlink. Get rid of the http:// or C:/ part of the address but keep all the surrounding parts of the code without the quotes "{HYPERLINK |" and the link should work as intended. The ones that say "current document" on mouseover are using a relative link.
Do this step before posting or exporting your final document, as the table of references will keep updating to the absolute link each time the table is refreshed.
Hope this helped. It took me a good while to figure this all out. Good luck out there!