You can use the Fax service through the Federal Voting Assistance Program (FVAP.gov). You will need to email your ballot or FWAB and any required supporting materials (see your state’s instructions) to email@example.com using the FVAP fax transmission coversheet here (scroll to the bottom of the page). FVAP will then fax your election materials to your Local Election Office. You should later verify that they were received OK with your Local Election Office.
And you can fax a document or photo from your smart phone too. For Android phones, see here (the app FaxFile has been recommended by a friend); for iPhone’s, look here or just search on something like “send fax iPhone free” and you’ll find some.