Is it permissible to propose to one of two sisters after having seen photographs of both of them through the sister, in order to avoid sensitivity between the two families?

The basic ruling is that it is not permissible to cast one's gaze upon women, even with the intention of marriage. However, it is permissible to look at the woman one intends to propose to, for someone who has decided to propose and expects her acceptance. There is no objection to looking at the pictures of the two girls to choose one of them, if you are determined to propose and expect her acceptance, knowing that the suitor is only permitted to look at the face and hands.