How can a lost phone, whose owner is known, be returned to him without the family's knowledge or arousing suspicions? Or should its value be given as charity instead?

Your friend must repent to Allah for the betrayal involving the phone and return it to its known owner, along with paying for its usage throughout the period she held it, because it is considered to be like usurpation (ghasb), and donating its value as charity is not sufficient. As for how to return it without anyone knowing, that varies depending on the circumstances.