Is it permissible to take money for a lost mobile phone, knowing that the sister was the cause of its being forgotten?

If your sister willingly gives you the value of the mobile phone, without any compulsion from you, then there is no harm in you accepting it, even if she is not obligated to guarantee it. This is because it would then be a gift from her to you, and the property of a person is not lawful [for another] except with their willing consent.