I assume by Ubuntu you mean the browser you are running on Ubuntu. So
we'll go with that: "favorites", more properly "bookmarks" are kept by
most browsers in an html file hidden deep in the filesystem. I don't
think IE does (no surprise), but IE does allow you to export "favorites"
into an html file. Once you do that, what happens next depends on what
browser you are using on Ubuntu. Some browsers have an import function,
some don't. I usually just move the file from the IE system (via
sneaker-net, LAN, whatever) to where the Ubuntu particular browser keeps
it's bookmarks. For my systems I use Firefox/IceWeasel and the
bookmarks are in:
/home/<username>/.Mozilla/Firefox/6jluxu4i.default/bookmarks.html (the
name of the "6jluxu4i.default" directory will vary by user). That's it.

BTW(1), make sure your browser is not running when you move the
bookmarks or they will be written over when the browser closes.

BTW(2), you might have to use the dreaded command line to do this.