Is it permissible to photograph a girl dressed in attire that she claims to be a hijab and then publish her picture in Islamic forums for the purpose of da'wah (inviting to Islam)?

What the young man did by photographing the girl with his mobile phone and publishing it online is impermissible. The prohibition is further emphasized if any part of her body was exposed or if it was done without her knowledge. He must remove the image and repent to Allah.