This story is printed by many newspaper and other media, I still couldn't find any source in Padma Purana yet.
Instead as per the sources given at this URL , the story of termination of Shree Rama Avatara in Padma Purana is different.
Taking a hint from Shri Rama, Vibishana, Sugriva, Jambavan, Hanuman,
Neela, Nala, Sushena and Nishada Raja Guha arrived. ...