Is it beneficial for the deceased if they are prompted with: "Allah is my Lord, Islam is my religion, and Muhammad is my Prophet" after their death, and if the order of the phrases is changed?

What you did is called "talqin" (instructing the deceased). Instructing the deceased before burial is not something we know to have a legal basis in Islamic law, nor has any scholar affirmed it. What a group of jurists have deemed preferable is to instruct the deceased after burial, based on the hadith reported by Al-Tabarani — though its chain of narration is weak — which states: "When one of your brethren dies, and you have leveled the earth over his grave, let one of you stand at the head of his grave and say: 'O so-and-so, son of so-and-so...'" The Shafi'i school of thought has explicitly stated that instructing the deceased (other than a child) is a Sunnah and should take place after burial.