Not sure what issue you're seeing. I just registered through Firefox and successfully created an account. Then, I logged out and re-logged back in with Facebook.
After I registered, I saw the invitation module, and everything worked normally for me. What happens when you say "It doesn't work". Do you get an error, blank area, click but no response, etc?
Also, can you let us know what version of Firefox you're using as well as what operating system?
Thanks,
Alex