This area of law is complicated because you are dealing with several conflicting sources of law.
Under Texas law you can possess a firearm just like the judge said.
The Federal firearms law says a person "convicted" of a felony can never possess a firearm. "Convicted" for federal criminal purposes does not include a Texas deferred adjudication.
Army regulations will determine what the Army considers to be a conviction or not, and what is an acceptable conviction and what is not. You should talk to a recruiter about what exact reason they are denying your enlistment.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.
Here is another way to look at it.
All 50 states must follow the federal gun law possession ban. In Texas, when you are looking to possess a gun, you will run into it as well. Even the Army (Navy, Air Force, Marines, Coast Guard), will follow federal law that considers your state jail felony "deferred" as a prohibition to your eligibilty.
Federal law prohibits gun possession by any of the following groupings of people. This is true no matter what Texas law says:
(1) Convicted in any court of a crime punishable by imprisonment for a term exceeding one year;
(2) Fugitive from justice;
(3) Unlawful user of or addicted to any controlled substance;
(4) Adjudicated as mentally defective or has been committed to a mental institution;
(5) Alien illegally or unlawfully in the United States or an alien admitted to the United States under a nonimmigrant visa;
(6) Discharged from the US military by dishonorable conditions;
(7) A former citizen of the United States who has renounced US citizenship;
(8) Subject to a court order that restrains the person from harassing, stalking, or threatening an intimate partner or child of such intimate partner; or
(9) Convicted of a misdemeanor crime of domestic violence
.... cannot lawfully receive, possess, ship, or transport a firearm.
If your convictions fall into any of these groupings, as a practical matter under federal law, you can never legally own a gun again no matter what Texas law says. So what if the paper you have says something different? If you violate federal law you go back prison. You are a convicted felon. You can never lawfully receive, possess, ship, or transport a firearm.
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