Is it permissible for a man to offer condolences to a woman, or for a woman to offer condolences to a man?

Consoling a Muslim for his brother is a Sunnah for both men and women. However, Islamic law blocked the door to temptation (fitna). Scholars stipulated that a man should not console a young woman unless she is one of his mahram (unmarriageable kin). As for an elderly woman, some scholars permitted consoling her due to the absence of fear of temptation with her, unlike a young woman. However, it is still better to refrain from consoling her as well. Books of Fiqh (Islamic jurisprudence) and the various schools of thought have mentioned statements affirming this.