TexasCHLforum.com

The only differences boil down to the driver license used on the application and whether or not there is a $25 change of address fee.

When a person still resides in a different state, that state's driver license number is used for the Texas non-resident CHL application process. Then, after the person moves to Texas and establishes residency, the person needs to get a Texas driver license and submit a change of address for the CHL that includes the change of driver license. This requires the $25 change of address fee, of course.

If one becomes a Texas resident first, then I'd suggest getting the Texas DL first, and then submitting the CHL application with the TX DL number and the new Texas address. This means there is no $25 change fee.

As long as a person has a different non-resident license available to keep carrying in Texas while waiting for the Texas CHL application process, then it is no problem to wait until the person gets here to apply. However, if the person's home state or other non-resident handgun license becomes void when moving to Texas (or is not recognized by Texas), then it makes sense to get the Texas non-resident before moving here so there is no "gap in coverage".