All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The Hadeeth that you have referred to in the question has no origin in the standard Sunnah books. It is, apparently, a fabricated, inauthentic Hadeeth.
Another similar saying refers to the last Friday in Ramadan as ''expiation Friday." Those who consider it authentic believe that if five extra prayers are performed on that day, they will make up for the prayers that have been abandoned all over that year.
All of these sayings are invalid, have no origin in the Sharee`ah, and are considered a Bid‘ah (religious innovation) innovated by those who neglect their prayers.
Every Muslim has to avoid this and warn others against it.
Allaah Knows best.