Question: Is it correct for one who is in the state of i’tikaaf to teach someone or (even) give a lecture?
Response: That which is better is for the one in the state of i’tikaaf to busy himself with specific acts of worship such as dhikr (remembrance of Allaah), prayer, reading the Qur.aan and that which is similar. However, if there is a need to teach someone or to learn, then there is no harm in this as this is (also) from the remembrance of Allaah.
Shaykh Ibn ‘Uthaymeen
Fataawa Ramadhaan – Volume 2, Page 876, Fatwa No.863
Fataawa Shaykh Ibn ‘Uthaymeen – Volume 1, Pages 549.fatwaonline.com