What is proven from the Prophet (blessings and peace of Allah be upon him) is that when he had finished praying, he would ask Allah for forgiveness three times, then he would say: Allaahumma anta as-salaam wa minka al-salaam, tabaarakta yaa dhaa'l-jalaali wa'l-ikraam (O Allah, You are as-Salaam (the One Who is free from all defects and deficiencies) and from You is all peace, blessed are You, Possessor of majesty and honour).
This is based on what has been explained previously in the answer to question no. 104163
After searching we could not find any proof for the duaa' mentioned by the questioner that is said after the obligatory prayer when placing the right hand on the forehead.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked:
There are some people who, after finishing the prayer, put their hands on their foreheads for a while and they say that this is Sunnah. Is what they say correct?
He replied: There is no basis for that as far as we know. There is no basis for placing the hands on the forehead after prayer.
End quote from Fataawa Noor ala ad-Darb.
And Allah knows best.
Reproduced from Islam QA