That painting is called The Storming of the Teocalli by Cortez and His Troops. It was painted in 1848 by the American painter Emanuel Leutze. Obviously that is considerably later than the actual conquest (it was also painted in Düsseldorf, Germany).

Leutze was informed by Prescott's 1843 book The Conquest of Mexico, which modern historians consider to be somewhat outdated, to say the least. I do not recall if it was published with illustrations, either in 1843 or subsequently.

The best book on American depictions of European-Indian encounter remains in many ways the exhibition catalogue The West As America. For more on Leutze I recommend Wierich, GRAND THEMES: Emanuel Leutze, Washington Crossing the Delaware, and American History Painting.

Edit: formatting