If you're using DSM4 and are also using a reverse proxy in front of your Synology, "Share file link" might not work, specifically if your Internet-facing port differs from the Synology port.
E.g., a "shared link" might look like this:
https://192.168.1.1:5001/fbsharing/2bKKwfXE
From the Internet, one could have requested the file by using:
https://1.2.3.4:5678/fbsharing/2bKKwfXE
However, after the request the response will be a redirect to
https://1.2.3.4:5001/fbdownload/index.html?k=2bKKwfXE. And because
5001 is not opened on the reverse proxy (or firewall for that matter), this
won't succeed.
In stead of using the proposed link, try to use:
https://1.2.3.4:5678/fbdownload/index.html?k=2bKKwfXE
UPDATE #1: Although the download will succeed, the suggested filename
might be index.html and not the original filename the file had.
Solution: rename the file after the download. This might only be the case when
the file is password-protected.