There is a Javascript that select all , just go to the invite your friends page and past following javascript into your Browser adress bar , hit enter .Depends how many friends you have it can take some seconds .

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

These méthode is a well known and outdated and could not work as Facebook invent the 50 Friends limit to "Suggest to friends " invite so you should not invite more than 49 Friends at once, as they will not receive your invitation.  A work around is making list with 49 Friends in it . Other alternative is a Greasmonkey Script for Safari Chrome that let you chose how many to select (working) you need Select Friends Script  to installed  

Greasmonkey : 

Firefox: https://addons.mozilla.org/en-US/firefox/addon/748/

Chrome: https://greasemetal.31tools.com/

Safari : how to install Greasmonkey in Safari GreaseKit