What is the authenticity of the statement that the angel on the left [who records misdeeds] moves to the right during prayer, based on the wisdom that it is impossible to commit a sin during prayer?

This statement has no Shariah evidence, and the claim that a person cannot commit a sin while praying is incorrect. It is possible for a person who is praying to fall into disobedience, such as looking at something unlawful, or praying in a usurped place, or with usurped clothing.