If they tried him for murder, what would be the additional offense to make it a capital offense? Can they use his AK conviction or would that be not allowed?
Yes, definitely. Here's the relevant part of the statute.
Sec. 19.03. CAPITAL MURDER. (a) A person commits an offense if the person commits murder as defined under Section 19.02(b)(1) and:
(2) the person intentionally commits the murder in the course of committing or attempting to commit kidnapping, burglary, robbery, aggravated sexual assault, arson, obstruction or retaliation, or terroristic threat