The Texas Declaration of Independence was not inspired by the American Declaration of Independence but rather influenced by it.
The original purpose of the American Declaration of Independence was to proclaim that the Colonies were free and independent states from England, although there were no clearly defined goals for this new country. The document itself treated the history of America starting with its discovery in 1492 and ended with a list of grievances against King George III (formerly Great Britain) and his Parliament in 1776.
There are similarities in some fundamental principles between these two declarations; both stated that all men have natural rights to life, liberty, and property; both had a list of grievances; both had a statement affirming national sovereignty (independence). However, they had different ways of justifying their grievances against the British government. The American Declaration of Independence focused on a historical case for its claims, but it also appealed to a higher law above itself as a justification for independence from Great Britain.