I've never heard of file maker pro associated with apple at all... anywho.
Let me know if you need clarification on this at all.
Who does the client talk to the server? Is it by IP address or computer name? I'm going to be its probably by IP address. I can't remember where this is but I think it was edit / preferences/ connections / TCPIP or something similar, there you can set the address of the server. Make sure this is the new computer' s IP address or hostname.
