Is it permissible to contact a girl via "Facebook" to inform her of the intention to propose in the future after securing a job?

A man's conversation with a non-mahram (definition) woman when necessary is permissible, provided that the Islamic etiquettes are observed and temptation is avoided, as this is a serious matter. If you are secure from temptation for yourself, then it is permissible for you to write to her and express your desire to marry her. Otherwise, seeking safety for your religion is paramount, and you can inform her through an intermediary. It is recommended that dating and engagement occur after preparation for marriage, with an emphasis on choosing a woman of religious commitment and good character.