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.