Hakim al-Ummat Hadhrat Mawlana Ashraf ‘Ali Thanawi (may Allah sanctify his secret) writes:
It is wajib (obligatory) to reply to the salam which is written in a letter. This reply may be [given] in writing or verbally.
- The fuqaha (jurists) have said that in reply to the salam which is written in a letter, one may say عليكم السلام or even السلام عليكم
Adab al-Mu’asharat, page12, English translation by Majlisul-Ulama of South Africa