What is the name of the mosque known as "The Messenger's Mosque" in Medina, and are there photographs available of it?

There is no mosque in the city named "Mosque of the Messenger" other than the Prophet's Mosque (Al-Masjid an-Nabawi). Pictures of the mosque from the time of the Prophet, peace be upon him, cannot exist, because photography had not been invented then. As for pictures of the mosque after the invention of photography, they are abundantly available on the internet.