Is this a valid adoption?

A valid adoption cannot be cancelled. However in this case the son was 16 years of age at the time of adoption and as per the provisions of the Hindu Adoption and Maintainance Act, the child to be adopted should not have  completed the age of fifteen years, unless there is a custom or usage applicable to the parties which permits persons who have completed the age of fifteen years being taken in adoption.  So, if there is no such custom there then, the adoption can be cancelled on this ground also.

Slightly differing to adv. Archana on first opening line “valid” I have to add following;

S. 16 of Hindu Adoptions and Maintenance Act envisages a statutory presumption that in the event of there being a registered document pertaining to adoption there would be a presumption that adoption has been made in accordance with law

S. 11 (vi) of the Act, which records that the child to be adopted must be actually given and taken in adoption by the parents or guardian concerned with intent to transfer the child from the family of its birth to the family of its adoption. The give and take in adoption is a requirement, which stands as a sine qua non for a valid adoption. Here the son is not even living with adopted father !

One significant aspects is absent out of the two in your case, so in my opinion the alleged adopted son has possibility in his favour other than age restriction brought to your notice by Adv. Archana.