Reference: Fataawa Ramadhaan – Volume 2, Page 799, Fatwa No.802
Fataawa as-Siyaam libni Jibreen – Page 177
Question: What is the ruling regarding drinking tea or coffee after the two units (rak’atayn) of the night prayer?
Response: That is permissible since the duration of the night prayer is long, and the elderly become extremely exhausted as do those who have accustomed themselves to taking tea and coffee as a means of energy. However, if there is no need [in doing so], then it is better to leave it.
And Allaah [alone] has the Complete knowledge [of all affairs].