I have a Windows Server 2012 that I have shared a folder that is accessible from within our network. I am running into an issue with being able to access this folder from a remote computer on another network with no VPN in place, and would rather not have a VPN in place. I realize that this is less secure, but it is what my client is requesting. I have a public IP for this server and I am able to remote into it successfully, however I am still not able to access the shared folder. I have fully disabled the firewall on this system, and even temporarily disabled our firewall to make sure that it was not being caused by the firewall. Any ideas on how I can accomplish this?
You can open ports 445 and 139 on the firewall with static NATs from the external IP to the internal IP, but that would be very insecure and highly discouraged. It should work though, assuming they can also browse outbound on those ports (their firewall isn't blocking outbound access to 445 and 139).
Using a VPN or other means would be better. You could look at setting up a secure FTP site on the server with access to those files/folders or using something like WingFTP or similar to allow https access.
Even if you do open the necessary ports to enable Windows file sharing traffic in, you will be blocked as a client from almost any network from getting there, because these are some of the most highly blocked ports on the web, and for good security reasons. So even if you can accomplish this, you shouldn't.
Other better options:
Hope that helps.