Ref. No. 809 Alif
In the name of Allah the most Gracious the most Merciful
The answer to your question is as follows:
It is allowed in Islam to adopt a child for nutrition. Our Prophet Muhammad (saws) adopted Hazrat Zaid bin Harisah (ra). But one must keep in mind that the adopted child cannot take the place of a real son/daughter. According to shariah, the adopted child is a stranger to these pretended parents. He/she will not get share in their inheritance. Moreover, when he/she is mature they will have to do pardah too.
And Allah knows best
Darul Uloom Waqf Deoband INDIA