I followed instructions from this topic https://askubuntu.com/a/33703/13207 to move SWAP and enable it for hibernating. All works fine, the system recognizes the new SWAP, swap is the same size as RAM.
$ swapon -s Filename Type Size Used Priority /dev/sda2 partition 16382972 0 -1
Then I moved to this topic http://ubuntuhandbook.org/index.php/2014/04/enable-hibernate-ubuntu-14-04/ and found a command to test if hibernate works
After this I can see that the system is saving data to the disk (disk indicator flashes) and the system goes off. I previously checked and saw that there is 2GB of data to be save to hibernation.
But, when I try to turn it on, I get hang on the black screen with a cursor.
Anyone has idea why I cannot boot back from hibernate?