Adoption not showing up on baptismal record

We have a family where the mother is divorced and remarried. Her new husband has legally adopted her 2 children. Their oldest son was baptized but his record is showing his biological father on the baptismal record and not the father who adopted the child. She claims this information was given to the clerk 2 years ago when the adoption happened (I was not in the ward at the time nor in this calling). The head of household is correct but not the father to the boy. How do I get that updated?

You should be able to edit that in Leader and Clerk Resources. Go to the child's record and click on the Family tab. You can edit the father information there.

While it's probably true in this case, it should be noted that changing the parent should only be done after the adoption is final per General Handbook 33.6.12.