Final answer:
The Republic of Texas successfully attracted many American immigrants through land grants and received international recognition, managing to sustain its independence from 1836 to 1846.
Step-by-step explanation:
One success of the Republic of Texas government after its formation was its ability to draw tens of thousands of American immigrants to its territory. This influx of settlers was largely due to the government's policy of granting land to heads of households, which helped to populate and establish the young republic. Despite political tensions and potential conflict with Mexico, the Republic of Texas managed to preserve its independence from 1836 until its annexation by the United States in 1846. Moreover, the Republic of Texas secured international recognition from countries such as France, Great Britain, Belgium, and the Netherlands, which was a significant diplomatic achievement for the nascent Lone Star Republic.