Is a sister sinful if she knew about a girl's relationship with a man, and advised her indirectly without informing her family, and sufficed with supplication and entrusting the matter to Allah?

If it is proven that a girl is corresponding with a non-mahram man, she is engaged in a reprehensible act and a trial. The sister has done well by advising her, and she should continue to advise gently and wisely. Informing her family about her situation if she persists in her misguidedness varies in ruling depending on the circumstances, and it may sometimes become obligatory. Among the means of rectification is shunning, while considering the best interest.