What is the ruling on publishing caricatures that show girls wearing a fake hijab, and what is the ruling on exchanging them among colleagues at work, and are these drawings considered unalluring and not provocative of desires?

The শরعي (Shar'i) hijab is not merely a head covering while wearing something that exposes or describes the 'awrah (parts of the body that must be covered). The means of calling to Allah and enjoining good and forbidding evil must be legitimate, effective, and beneficial. Drawing animate beings by hand (caricatures) is not permissible according to Sharia. There are various legitimate methods of da'wah (Islamic propagation), such as Islamic tapes, pamphlets, and printed letters.