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.

Method 1

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

javascript:elms=document.getElementById(‘friends’).getElementsByTagName(‘li’);for(var fid in elms){if(typeof elms[fid] === ‘object’){fs.click(elms[fid]);}}

in the address url bar

Method 3

Same ad method 2 just paste this new script

javascript:fs.select_all();

These javascripts are not relaible as facebook keeps changing them so just go for the first method.