Is it permissible to express love for the sake of Allah through a gift upon which is written "I love you for the sake of Allah," or must it be verbal? And is it permissible to offer such a gift to a woman, such as a former teacher?

It is legislated for a Muslim to inform his brother of his love for him for the sake of Allah. This is a recommended act, not an obligatory one, and can be done through writing or oral communication. It is not legislated for a man to inform an unfamiliar woman of his love for her, out of fear of temptation. As for giving gifts to an unfamiliar woman, it is permissible as long as it does not lead to something forbidden or to temptation.