Final answer:
Stephen F. Austin was arrested because he sent a letter from Mexico to Texas, encouraging the establishment of a state government.
Step-by-step explanation:
The person who was arrested for sending a letter back to Texas while in Mexico, urging them to set up their own state government, was Stephen F. Austin. In 1834, the Mexican President Santa Anna dismissed the Mexican Congress and abolished all state governments, including that of Coahuila y Texas. Austin's actions were seen as a violation of Mexican law, leading to his arrest.