Does sin befall the mistress of the house if her Christian maid uses a mobile phone registered in her name to speak with friends from her own country?

If you gave her the phone without knowing or suspecting that it would be used for something forbidden, then there is no sin upon you, and the sin is upon her. However, if you knew or strongly suspected that she would use it for something forbidden, then you risk incurring sin because you contributed to the disobedience. It is forbidden to give a gift to someone if it is suspected that the gift will be used for an act of disobedience.

If the phone was a loan, you must warn her against using it for an act of disobedience. If she does not desist, then take it back from her, because a loan becomes forbidden if it aids in disobedience. Allah Almighty says: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression."