What is the expiation for the sin of a young man who impersonated a girl, causing another young man to become attached to him, which led to an accident involving this latter young man, taking into account the first young man's unwillingness to reveal his true identity to avoid psychological harm to the other party?

You must repent to Allah Almighty from lying, deception, and imitating women. This act is丑陋 and is practiced by those who do not fear Allah. It involves degradation and baseness, and stems from perversion and sickness. It is necessary to sever this forbidden relationship, change the email address, and delete the accounts. You may send a message to the other party informing them of your true identity so they know they were deceived.