How to transfer huge files between Android phones only with ES File Explorer and Wi-Fi?
If Es File Explorer doesnt work, I suggest that you use SuperBeam: https://play.google.com/store/apps/details?id=com.majedev.superbeam

It uses Wifi Direct Technology to transfer files at wifi speeds, and the wifi direct connection is initialized by scanning a qr code generated by the app of by touching them together with nfc on.  You can "Share" the file with Superbeam and opening the app starts the reciever end of the communication