This is the 1844 edition of the map of North America by the Society for the Diffusion of Useful Knowledge, showing the continent with Texas as an independent Republic.

Although dated 1843 on the map, that was actually the copyright date. The year of issue is actually 1844 and falls within the nine years (1836-45) when Texas was considered an independent Republic. This clearly marked on the map, with Texas having borders both the the United States and Mexico. Its eventual absorption by the United States a year later would rapidly lead to the Mexican American War of 1846. 

Further points to interest on this map is the yet-to-be settled border between the United States and British America or modern Canada, leading to the Treaty of 1846 which drew the border as it is today. California is still shown as part of Mexico and Alaska is Russian or "Russian America" as shown on the map. 

Original colour. [AMER2415]