My stepson has lived with us for 2 1/2 years his mother is still custodial parent and has not seen him in 5 months

We sure could use some more details. How is it that he came to live with you to begin with?

But normally abondoment is when the parent leaves them alone at walmart and drives off, or used in child suport cases for non payment.

What needs to happen now, is all of this has to be documented, and the non custody parent files in court for a change in custody.