Dear Client,
In adoption , under certain circumstances, consent of father not required - read below
Sec 9 The Hindu Adoptions and Maintenance Act, 1956
(3) The mother may give the child in adoption if the father is dead or has completely and finally renounced the world or has ceased to be a Hindu or has been declared by a court of competent jurisdiction to be of unsound mind.
AND in ur case biological father has abandoned the child, hence, adoption may be effective by order of the High Court.
One way out -
In one of the case - Hon`ble Supreme court has allowed an unmarried mother to apply for guardianship of her child without sending a mandatory notice to the father who did not have any ties with the child after its birth.
Case No. Civil Appeal No. 5003 of 2015
Case Title ABC v. The State (NCT of Delhi)
Bench - Justice Vikramajit Sen, Justice Abhay Manohar Sapre. Date of Judgment 6 July 2015
Following this ur wife can legally give her child in adoption.
ON lines of this judgement also she can validly give child in adoption without father consent.
ALSO refer - Kerala High Court
Sunilkumar vs Anila.V on 1 June, 2010 - supports ur case