Your roommate should be fine to remain at his residence, considering that you are over 2 miles from the park.
Texas law prohibits registered sex offenders from living within 500 feet of parks or certain other areas. It appears that your friend is well over the required amount of distance.
If the HOA has asked him to move, he'll need to file an objection, or write a counter letter citing the law I mentioned above and the fact that he is within the legal boundaries.
If for some reason the HOA still objects, he may need to hire an attorney to represent him against the HOA and get them to comply with all HOA by laws and TX state laws.
But yes, under state law he should be fine remaining at your residence.
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