Is it permissible for a female to include Salaam in her letter to a ghair mahram male and vice versa?

Answer

The Masnoon Salaam, i.e. Assalamu Alaikum, is not a statement of abuse. When necessity constrains a female to write a letter to a ghair mahram male, her letter contains numerous statements. There is nothing preventing her from including the Salaam among the many statements. The prohibition of offering Salaam to a woman and vice versa applies when the Salaam is made verbally in the presence of one another. According to the Qur'aan, the voice of a woman also constitutes an element of fitnah, hence the prohibition. Since this fitnah is absent in a letter, she may write the Salaam.