The Mother would have to file a Petition to Modify the custody order. A 16 year old child does not have absolute authority to choose which parent to live with, but unless there is a problem with the child, his wishes will be very persuasive.
To make this happen, the Mother needs to fill out and follow the instructions on this form: http://courts.phila.gov/pdf/forms/domestic-relations/prose-pet-to-modify-custdy.pdf
Everything the mother needs is in that link. She is the Petitioner, Father is the Respondent. For number 4, she should just state that the child wishes to reside with her and that she is able to care for him.
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