Please find the answer of your problem.
First you need to check your connection string which is embedded in your program. You would not added server name in connection string. If there is look like as connectivity to firebird database
'DRIVER=Firebird/InterBase(r) driver; UID=****; PWD=*****;'+
You need to specify in dat file your server ip. And one thing is your database folder must be shareable to accessing user. Then you can simply access the connection from server database.
Here is a small source code for connecting multiple systems through a single database server.
Constr = 'DRIVER=Firebird/InterBase(r) driver;UID=XXXXX;PWD=XXXXX;'+
ADOConnection1.ConnectionString := constr;
ADOConnection1.Connected := True;
If ADOConnection1.Connected then
ShowMessage('Connection is active');
ADOQuery1.Connection := ADOConnection1;
ADOQuery1.SQL.Text := 'Select * from Test';
ShowMessage('Total Records = '+IntToStr(ADOQuery1.RecordCount)+' '+ ADOQuery1.Fields.AsString);
Here 'DBNAME=192.*.*.*: C:\Program Files\Database\EXAMPLE.FDB'
This is database server ip address, and rest of server database path