Peace Be Upon Allah

In this post I present a hadith. My translation as the English version leaves chunks of Arabic untranslated.

Umar b. Hafs told us, my father told us, Al-Amash told us, he said: Shaqiq told me, from Abdullah. He said: When we used to pray with the prophet, Allah pray for him and salute him, we said: Peace be upon Allah before his slaves, Peace be upon Jibril, peace be upon Mikal, peace be upon so-and-so, and when the prophet, Allah pray for him and salute him, left, he turned his face towards us and said: Allah is peace. So when one of you has sat in prayer, let him say: Greetings to Lah, and prayers and good things and peace be upon you, prophet, and Allah's mercy and his blessings, peace be upon us and upon Allah's righteous slaves. For if he has said that, it has struck every righteous slave in the sky and the Earth. I bear witness that there is no god but Allah and I bear witness that Muhammad is his slave and his messenger. Then he may choose after that from the words what he has willed.

https://sunnah.com/bukhari:6230

'When we used to pray with the prophet'. So they would repeatedly say, 'Peace be upon Allah' in the 'prophet's' presence. 'Greetings to Lah? 'Bearing witness' that 'Muhammad' is Allah's slave and messenger' is part of their prayer? He may then choose after that what he wants to from the words?