Is it permissible for parents to send their daughter's picture to the suitor's family for them to see and return it, especially if they are in different cities?

It is permissible for the girl's family to send her picture to the suitor's family, provided that no one manipulates it, and that its viewing is restricted to women, after which it is returned to her family. There is no harm in the suitor seeing the picture, provided that his gaze is for inquiry and not for pleasure, and that he predominantly expects to propose if he is pleased with her. However, one should not rely solely on the picture, because the Sunnah is to look directly at the prospective bride, as this strengthens affection and love between them, based on the hadith of Al-Mughirah ibn Shu'bah regarding his engagement: "Look at her, for it is more likely to bring affection between you two."