Is it permissible for a sister to inform her husband, who is a sheikh, about the condition of her brother who watches pornography and has abandoned prayer, so that he may advise him without his knowledge? And is this considered backbiting?

Watching pornographic websites and abandoning prayer are forbidden (haram). You must advise your brother and denounce his actions. You must conceal his faults unless informing your sister's husband is the only way to eliminate the wrongdoing. In that case, you may inform him, taking the necessary precautions so that your brother does not discover the matter. This is not backbiting (gheebah) that is forbidden, as it falls under sincere advice in religious matters. Be sure not to be drawn into this affliction yourself.