State law says a convicted felon may not possess a firearm within five years after conviction and before the fifth anniversary of the person's release from confinement following conviction of the felony or the person's release from supervision under community supervision, parole, or mandatory supervision, whichever date is later; or after this time period, at any location other than the premises at which the person lives. (TX Penal Code 46.04)
But Federal law says that: "[i]t shall be unlawful for any person (1) who has been convicted in any court of, a crime punishable by imprisonment for a term exceeding one year ... to ship or transport in interstate or foreign commerce, or possess in or affecting commerce, any firearm or ammunition; or to receive any firearm or ammunition which has been shipped or transported in interstate or foreign commerce." (8 United States Code 922(g)(1))
So the answer is that even if you are not violating Texas law, you are still subject to arrest for violating federal law if you have a shotgun.
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.
The first question is was the person convicted? If the person did a deferred probation and lived it out then it would not count as a conviction for the possession under Texas law. However, if he or she was finally convicted then the only place he or she could have the firearm was in his or her home. However, this can still be a violation of federal law if the weapon was not made in Texas.
I agree with the other contributors. Under Texas law, a felon cannot own or possess a firearm for 5 years. After that, under state law, a felon may possess a firearm in his or her home. A convicted felon cannot possess a firearm under federal law.