There are a number of methods that you can use to select all the friends for inviting as facebook makes it compulsary to select all friends individually.
You need to have Google Chrome. The install an extension called Facebook Invite All from here https://chrome.google.com/extensions/detail/eibdjcmcmfggjoiaaoojhicjnkghbkbe
Once this is installed then you can go to your invite page and you will see and option of select all friends called TOGGLE ALL, see sample pic below
Method 2 (Is it working now?)
When you open your invite page just copy and paste
in the address url bar
Same ad method 2 just paste this new script