For different religion there are different adoption laws. For Hindus Indian system follows The Hindu Adoption and Maintenance Act, 1956. Section 6 of the HAM Act 1956 lays down the following 4 requirements
1. The person who is adopting must have the capacity and the right to adopt.
2. The person who is giving the child in adoption must have the capacity to give.
3. The person who is being adopt must be eligible to be adopted.
4. The adoption must satisfy all the rules given in this act
These are the requisites of adoption. The adoption act doesn’t talk about any legal documents. But there are conditions which need to be fulfilled for adoption. For eg the difference between the age of the adoptee and the adopter should be 21 years. So if all the conditions are met according to Hindu Adoption and Maintenance Act, 1956 then it would be a valid adoption though there is no legal document for it. According to Section 12(b) any property which vested in the adopted child before the adoption shall continue to vest in such person subject to the obligations, if any, attaching to the ownership of such property, including the obligation to maintain relatives in the family of his or her birth. So he has right over the property both the ways. Until and unless you prove that the adoption is invalid.