Adoption of spouse's adult children

I have been asked to add adult children that were adopted after a second marriage to the adopted father's family list in his membership record. The children are not in my ward. Is this something I am able to do, or does it need to be done by their membership clerk?

Assuming the father is in your ward, and the adoption is final, you should be able to do it. However, you'd need information on the children (assuming they are members) to link them up.