Is the following Hadeeth authentic: "Anyone who fasts Ramadhaan then follows it with fasting six days in Shawwaal will gain reward as if he fasted the whole year."? May Allaah reward you.

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.

This is an authentic narrations that was reported by Ahmad and Muslim and was transmitted on the authority of Abu Ayyoob Al-Ansaari .

In another narration, on the authority of Thawbaan the Prophet stated that anyone who fasts six days in Shawwaal after the 'Eed day of Ramadan will be considered as if he fasted the whole year, because every good deed will be multiplied tenfold in reward. [An-Nasaa’i, Ibn Hibaan and Al-Bayhaqi]  Both Hadeeths are authentic.

Allaah Knows best.