As salamu aleykum, What is the proof of the Hanafi Fiqh of school of giving only one taslim to the right side before performing sajdah sahw? Was salaam

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

We have already issued Fatwa 89411 clarifying the method of prostrating for forgetfulness according to the Hanafi School of jurisprudence and that it is after saying Salaam (i.e. concluding the prayer).

However, this School has many views regarding saying Salaam for someone who is obliged to prostrate for forgetfulness, whether he should say Salaam once [to the right hand side only] or twice [to the right hand side and left hand side]. Some of their scholars are of the view that a person should say Salaam only once; their evidence is that the first Salaam to the right side is enough to conclude the prayer and the second is intended for salutation and when prostrating for forgetfulness, there is no need for it. Therefore, one should not say the second Salaam, but if he says it, then the prostration for forgetfulness is waived. As far as we know, they do not have any evidence to prove this.

However, other scholars of the Hanafi School of jurisprudence are of the view that one should say Salaam twice and then prostrate for forgetfulness. Some scholars of this School are of the view that anyone who says that it is an obligation to say only one Salaam, is among the innovators. 

Allaah Knows best.