Is it permissible for a woman to keep a picture of her suitor on her phone to look at it without lust, or is that not permissible because he is a stranger (non-mahram)?

It is permissible for the fiancée to look at her fiancé and vice-versa, and it is permissible to repeat the gaze if there is a need for it. There is no objection to a woman looking at a picture of the man who wishes to propose to her, and repeating the gaze until acceptance or rejection occurs. However, the picture should not be kept if the need for it is no longer present.