Al-Adab Al-Mufrad, Book 45, Hadith 1 (In-Book) ⓘ

Ibn 'Abbas said, "I think that answering a letter is a duty, just like returning the greeting."

حَدَّثَنَا عَلِيُّ بْنُ حُجْرٍ، قَالَ‏:‏ أَخْبَرَنَا شَرِيكٌ، عَنِ الْعَبَّاسِ بْنِ ذَرِيحٍ، عَنْ عَامِرٍ، عَنِ ابْنِ عَبَّاسٍ قَالَ‏:‏ إِنِّي لَأَرَى لِجَوَابِ الْكِتَابِ حَقًّا كَرَدِّ السَّلامِ‏.‏

sunnah.com

also referenced under: Hadith 1117 (Reference) & Book 45, Hadith 1117 (English)