Is it true for a person to say that "all Muslims are messengers"?

A Muslim must believe that Allah concluded His messengers with Muhammad, peace be upon him, and that there is no messenger or prophet after him, as Allah Almighty said: "Muhammad is not the father of any of your men, but he is the Messenger of Allah and the Seal of the Prophets." Whoever claims otherwise is a liar and contradicts the creed of Islam.

Perhaps the intent behind the statement "every Muslim is a messenger" is that Muslims are tasked with inviting people to Allah and conveying His message after the Prophet, peace be upon him, as Allah Almighty said: "Say, 'This is my way; I invite to Allah with insight, I and those who follow me.'" And as the Prophet, peace be upon him, commanded: "Convey from me, even if it is a single verse."

It is better to call things by their true names. So, one should say: "Muslims are callers to Allah Almighty" or "Muslims are bearers of Allah's message to His servants," and avoid ambiguous expressions.