An employee is telling us that in Texas we are required to offer 24 months of cobra not 18 for a termination.

Is this correct?

If the plan is fully insured, you must meet any State regulations - contact the TX Commission of Insurance. Federal COBRA requirements are limited to 18 months for a termination of employment.

I believe Texas has a continuation provision which is applicable to group insurance policies and which allows certain individuals (and their families) to have 6 months of continuation.

According to the Thompson COBRA guide, the Texas law states that coverage under it ceases if the individual is eligible for similar coverage under Federal law. So if the individual is eligible for COBRA under the Federal regs, they aren't eligible for Texas continuation which is only 6 months in the case of termination or 12 months in the case of divorce or death.