Filezilla has the option of storing all your FTP connections through site manager. You can access the site manager from File -> Site Manager or CTRL+S. When you open this you can see all the FTP connections you have stored so far. When you have a situation where you have to use all these FTP connections to another machine or Laptop, Filezilla has the option of exporting all you connections through an xml file. Here are the steps which will help you do this,
1. Open up your Filezilla FTP Client (Version can be 2 or 3)
2. Click File -> Site Manager
3. You will get the screen as below (for security reasons I am not showing all my connections)
4. Click File from this window (you can see this at the top)
5. When you click File you get the options Import and Export as shown in the screenshot below
6. Click Export and then with all details, you will be asked for a file name to store these FTP connections.
7. This will now store all your FTP connections in an xml format.
8. Use this xml file in a machine where you need these details and open Filezilla and follow the above process and now instead of Export you will have to select Import and select the xml file to get the all the connections details.