In the comics, Falcon has not taken on the mantle of Captain America. Captain America is usually depicted as Steve Rogers or other established characters in the traditional storylines.
In certain comic arcs, Falcon took on the mantle of Captain America. This happened as part of evolving storylines and character developments within the comic universe.
Falcon doesn't become Captain America in the comic universe. The mantle of Captain America has its own established history and succession that doesn't include Falcon.