Is he considered responsible for the girl if his friend kisses her after she left him? And is he obligated to inform her family to protect her? And what is the expiation and punishment for what he did by kissing her?

It is not permissible for a man to have a relationship with a woman who is unlawful to him, and he must sever this relationship and repent to Allah. Kissing between a man and a woman who are not mahram is forbidden and considered a minor form of adultery committed by the limbs. Its expiation is sincere repentance, seeking forgiveness, and increasing in righteous deeds. Allah Almighty says: (Indeed, good deeds do away with evil deeds.) The Prophet, peace and blessings be upon him, said: "And follow up a bad deed with a good deed, it will erase it."

Regarding your responsibility towards the girl and your friend, if you can advise them to cut off the forbidden relationship, then do so. If they respond, do not inform the girl's family as a cover for her, and let your advice to the girl be indirect, through righteous women. If they do not respond, you may inform her brother if you find no other way. We advise you to associate with good people, attend gatherings of knowledge, and maintain congregational prayers in the mosque.