Will he who caused the spread of a photo-sharing social media application earn the sins of its users who publish pictures of women, and the sins of those who view these pictures?

The default ruling for creating shared programs and systems that might be used for both permissible and forbidden purposes is permissibility, unless it is highly probable that they will be used for forbidden purposes. In that case, creating them is not allowed. The same ruling applies to selling and gifting them.

Therefore, there is no sin upon you if you did not know at the time of gifting that they would use it for forbidden purposes. However, if you strongly suspect that, then it is not permissible for you to give it to them. You should also remind them that this is a reprehensible act and not permissible. If they insist, then there is no sin upon you regarding the pictures they upload.