Until the feds remove the disability, all a felon can do is POSSESS the firearm in his abode, insofar as Texas is concerned (after five years has transpired).
Texas allows the felon to vote, sit on a jury, etc...
Texas restores MOST of the rights a felon never regains in other states.
I belong to a trial lawyers association that advocates the complete restoration of all rights felons have lost after a waiting period, during which time the person demonstrates her/his ability to live life as a responsible citizen.
Texas doesn't allow the felon to "open carry", or receive a "ccp".
Former felons get popped in Texas frequently, confusing the right to own the firearm in her/his abode, with the right non-felons have to carry and transport a firearm.
Under Texas state law a convicted felon may possess a firearm in the residence, in which he lives, once five years have elapsed from the date his sentence was discharged. This means the later of release from prison or parole. This is not true under federal law. So, while a convicted felony could lawfully possess a firearm in these very limited circumstance under state law, he could possibly be charged and convicted under federal law, even though current federal policy is to defer to state law on this issue.
Under Texas Penal Code §§ 12.33, 46.04, the unlawful possession of a firearm is a third degree felony with a punishment range of two to ten years for a defendant with one prior felony conviction and fine up to $10,000.
In legal terms, the word "possession" is an abstract term, but Texas courts, like most other state courts, have the defined as the term as follows: "Possession means actual care, custody, control or management. Possession is a voluntary act if the possessor knowingly obtains or receives the thing possessed or is aware of his control of the thing for a sufficient time to permit him to terminate his control."
To be convicted as a felon in the unlawful possession of a firearm, the State must prove only that 1) a person, 2) who has been convicted of a felony, 3) possessed a firearm, 4) after conviction and before the fifth anniversary of the person's release from prison or parole or other community supervision. Under Texas Penal Code § 6.01(a), the State must also prove the defendant voluntarily possessed the firearm.
There is only ONE way for a felon to FULLY regain all of her/his rights to possess/transport/carry/use a firearm in Texas, that is obtaining a full pardon. Given the very limited number of pardons issued from the governor's office, a pardon is extremely unlikely.
A Texas lawyer offers additional discussion of the question at hand:
Federal felon in possession of a firearm statutes (prohibited person)… Sherman & Plano, TX Criminal Defense Lawyer