Is it permissible to wake someone for Fajr prayer via a phone call without speaking, knowing that there is a severance of ties between you for the sake of Allah?

You did well by not speaking with the non-mahram man. Sound repentance involves abandoning the sin, regretting it, and resolving never to return to it. Part of sincere repentance is avoiding the causes of disobedience, blocking its paths, and eliminating the root of evil. Contacting this man by phone could be from the steps of Satan; therefore, all ties with him must be severed. If he is interested in marriage, then let him propose to you through your guardians.