You won't be able to do this with simple port forwarding in your router. When www.company.com and fm.company.com both resolve to the same IP address in DNS, there's no way for a router to distinguish the requests so that the router forwards to the right internal server. All the router knows about is IP addresses and port numbers, so a request for fm.company.com looks just like a request for www.company.com.
If you have more than one public static IP address, you may be able to configure your router for 1:1 NAT, so that one of your static IPs translates to your web server, and another of your static IPs translates to your FM server. You'll need multiple static IPs from your ISP, however, and a router that supports 1:1 NAT.
If you only have one static IP address, or if you're using some kind of dynamic DNS service, you might be able to accomplish what you want by configuring your second web server as what's called a Reverse Proxy. In that configuration, your new web server would have one virtual host for 'www.company.com', handling requests as normal. Then you'd have another virtual host on the same server, responding to 'fm.company.com', configured as a reverse proxy for whatever internal IP address your FM server has. You'd forward all incoming traffic to the new web server, and it would either handle a request for "www" itself, or forward a request for "fm" to your FM server.
Configuring Apache for that is simple, though it can be tricky when dealing with reverse proxies. I have no way of knowing what your server configuration is like, so I couldn't give you specific advice. But let's say your FM server has an internal IP address of 192.168.1.11. The Apache config file for your proxy virtual server would probably look something like this:
<VirtualHost *:80> ServerName fm.company.com ProxyPass / http://192.168.1.11:80/ ProxyPassReverse / http://192.168.1.11:80/ </VirtualHost>
The traffic would then come through your router, to the new web server, then over to your FM server, then back to your web server and back out through the router. All the magic happens on your internal network, on your new web server.
If you're using SSL, things are slightly trickier, but still feasible.