Legal Question in Criminal Law in Texas

Yes he can. Here is the relevant statute:

(a) A person who has been convicted of a felony commits an offense if he

possesses a firearm:

(1) 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

(2) after the period described by Subdivision (1), at

any location other than the premises at which the person lives.

(b) A person who has been convicted of an offense under

Section 22.01, punishable as a Class A misdemeanor and involving a

member of the person's family or household, commits an offense if

the person possesses a firearm before the fifth anniversary of the

later of:

(1) the date of the person's release from confinement

following conviction of the misdemeanor; or

(2) the date of the person's release from community

supervision following conviction of the misdemeanor.

(c) A person, other than a peace officer, as defined by

Section 1.07, actively engaged in employment as a sworn, full-time

paid employee of a state agency or political subdivision, who is

subject to an order issued under Section 6.504 or Chapter 85, Family

Code, under Article 17.292 or Chapter 7A, Code of Criminal

Procedure, or by another jurisdiction as provided by Chapter 88,

Family Code, commits an offense if the person possesses a firearm

after receiving notice of the order and before expiration of the

order.

(d) In this section, "family," "household," and "member of a

household" have the meanings assigned by Chapter 71, Family Code.

(e) An offense under Subsection (a) is a felony of the third

degree. An offense under Subsection (b) or (c) is a Class A

misdemeanor.