Can This Be Done????

Yes, just like local file sharing... except that it's a lot slower, and the complications of using outside IPs, Forwarding Ports from Routers, etc.

Have them make a zip of their file, and e-mail you the zip file. If the message bounces, check with the internet service provider on both end what is the maximum mail attachment size they will allow, and send in smaller chunks.

That would get over any hurdles such as setting up protocols, VPN or network mountable volumes, and prevent you from having to monitor your IP address at the moment they try to connect to you, or get a dyndns account.

Just ftp them

That requires you know their IP address at the time you FTP them.

Yes, but if you need to ask how it is probably simpler to pay your friend a visit (unless they're quite far away)!

The issue you have is that you want to shar files over a LAN not the internet. The safest way to do this would be via a VPN and that would that the internet out of the equation essentially.