You'll be covered to the limits of that policy, but it doesn't necessarily mean that you'll meet Texas' insurance standards. You might be required to have more coverage, or different coverage, and if you get into an accident, you'd have a problem. That being said, I don't recall that Texas' requirements are particularly stringent (I lived there for 43 years), so you may be fine. However, it's best to find an agent locally and make sure you're covered; chances are, all you'll have to do is change your address, and maybe adjust your coverage amounts.
I had to go through it when I moved to Washington state, but it wasn't a big deal; one coverage went up, and another went down, and all in all, my cost has been just about the same.
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