Am I obliged to guarantee a phone that was forgotten in a taxi and had a manufacturing defect, and to appease its owner by buying a new phone, or is my cousin who handed it to me the guarantor?

The hand of the one who asks is a hand of trust (amanah); therefore, he is not liable unless he transgresses or neglects. The loss of the mobile phone due to the questioner's forgetfulness is considered negligence, which necessitates liability according to the majority of jurists. Compensation shall be in kind if available, otherwise, it shall be with the value determined by experts.