It's unfortunate, but my strong belief is that there was a simple miscommunication between the clerk of court and the firearms agency.
If you had an attorney representing you on the DUI charge, they may be able to help you out here as well.
Regardless, contact the firearms agency. There phone number and/or website address are likely on the letter you received. Explain that the sentencing included that you ARE permitted to possess a firearm, it is simply limited to hunting purposes only. If they only require a copy of your judgment/conviction, simply make a copy from the papers you were provided in court and forward that to them. If they required a certified copy, you will need to contact your local clerk of court to request that they print out a copy and certify it for you.
To address a concern you stated, you should NOT need any caselaw or precedent to address this matter, it is simply a matter of clearing up the discrepancy between your sentence and the action taken by the firearms bureau.
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