Is written communication permissible between a young man and a young woman who are not mahram, with the intention of marriage after her family's permission?

There is no harm in communicating with a girl to express a desire for marriage, provided that it is limited to what is necessary, avoiding expressions of love and flirtation, and ensuring safety from temptation. If she agrees, she should be betrothed through her guardian, and communication with her should cease until the legitimate marriage contract is performed. It is obligatory to seek a woman of religious commitment and good character, to inquire about her from trustworthy individuals, and to seek guidance from Allah (istikharah) concerning her.