What is the ruling on giving a baby girl to a barren sister, with the agreement of both spouses?

There are two scenarios for giving this child to this sister:

The first is that it is an act of kindness and upbringing without attributing her lineage to them. This is permissible if she is raised well.

The second is that it is in the form of adoption, attributing her lineage to her and her husband. This is forbidden by Islamic law.