What is the ruling of Islamic law on a relationship of brotherhood that developed between a young man and a young woman who are brought together by da'wah (Islamic propagation) activities, and which evolved to include checking on each other via phone, while adhering to sharia controls?

It is not permissible for a man and a woman who are not mahram (definition) to establish any relationship between them, for even if it appears innocent, it is from the steps of Satan and his enticement. Allah Almighty has warned against mixing with women, and commanded that they be asked from behind a veil, and forbade softening the speech. The temptation of women is among the greatest and most dangerous temptations, as stated in the Hadith (definition): "I have not left behind me any temptation more harmful to men than women." Therefore, these relationships must be severed, and the permissible and safe alternative is communication through their mahrams.