Is it obligatory for someone who has published a fatwa prohibiting women or girls from posting pictures of men on Facebook to ask his friends to spread it likewise, or is it sufficient to advise only those who directly follow him for fear of embarrassment?

It is not permissible for a woman to post a picture of herself with her face uncovered on websites where non-mahram men can see it, nor to use a picture of a non-mahram man as her profile picture. You are not obliged to inform your friends about spreading the fatwa, but doing so is good. Do not be concerned by the blame of those who criticize spreading knowledge with wisdom and good counsel.