Here is the question presented to the court:
Does the Full Faith and Credit Clause of the Constitution require that the Alabama state courts recognize a Georgia state court’s adoption order?
Here's the court's decision:
The Alabama Supreme Court erred in refusing to grant full faith and credit to a judgment by a Georgia court making a woman the legal parent of the children she had raised with her same-sex partner since birth; the judgment appears on its face to have been issued by a court with jurisdiction and there is no established Georgia law to the contrary.
For detail:
Scotusblog: V.L. v. E.L.
Oyez: V.L. v. E.L.