VNC Connection

https://portforward.com/fritz-box/

Basically you open ports 5900 (VNC) and 3283 (ARD Control Port) and forward external (WAN-side) traffic to whatever device you wish to connect to on the private (LAN-side) of your firewall. Your firewall is the Router. All Routers/Firewalls do port forwarding slightly differently and no-one here can tell you as the way this is done varies from device and manufacturer. Best to look for support on the manufacturers website or the manual that comes with your device.

There's no "Apple Server" to install here, unless you're referring to the macOS Server.app package that adds various network services to macOS, and that's not particularly related to the in-built screen sharing app nor to Apple Remote Desktop app.

With the upcoming release, the macOS Server.app is also deprecating a number of the network server features that various folks use. But that's fodder for another discussion.

Apple Remote Desktop is also a client and not a screen sharing server, and it's not necessary for remote access into a macOS system, Both the built-in screen sharing client and the Apple Remote Desktop client use the same in-built screen sharing server in macOS.

If you're trying to access your system remotely as is implied by the reference to the router, you'll need to ensure the necessary TCP ports are open and forwarded to the target system. TCP 5900 is one of the ports used.

Your ISP will also have to allow remote inbound access. Some ISPs will firewall server-oriented ports. Some ISPs that firewall those ports will open them on request, others will not. Various ISPs do not firewall those ports. Best diagnostic there is to see if the remote access is hitting the firewall, which usually involves looking in the network firewall logs. Those logs would be on the Fritzbox, in this case.

VNC is not usually used with macOS, and there can be some settings tweaks required for that connection.

Once you open TCP port 5900, then whatever system or server is behind that port forwarding will be deluged with probes and attacks. Ensure that your passwords are secure, and expect that your log files can sometimes get pretty busy with the activity. Dictionary attacks can go on for hours or days, if folks are interested enough in the access. And the attackers are often using compromised systems, so the costs of these attacks are very low for the attackers.