During the entire first film, Boromir wore arm armor with the symbols of Gondor. Before the death of Boromir, Aragorn promised him he wouldn’t let Gondor fall. When Boromir heard these words, he accepted Aragorn as his king. When Boromir died, Aragorn took his arm armor.
This scene is in the film, but it only lasts for about 2 seconds. And it’s more about the feelings of Aragorn, rather than about the armor. In the future, this fact is not highlighted but Aragorn wears the armor in almost all of the fights, right up until the end of the story.