Most Texas employers handle claims for unemployment compensation in-house (i.e., they don’t use an outside lawyer).  A good resource to consult when handling these claims (and for answers to many Texas specific employment-related legal issues generally) is published by the Texas Workforce Commission titled "Especially for Texas Employers".  According to its introduction, 

Especially for Texas Employers has been written to explain the sometimes confusing "legalese" of federal and state employment law in easy to understand language that makes sense in the everyday business setting. This publication is an effort to bring you the kind of information and assistance that you can use on a daily basis, and which you as a taxpayer deserve. 

ETE contains sections on: Hiring: Basic legal Issues for Employers; Pay and Policy Issues; Work Separation Issues; Post-Employment Problems and a resouce page Employment Law-Related Web Sites.  Guidance related to handling unemployment benefit claims is found under Post-Employment Related Problems. 

Follow me on Twitter @RussellCawyer.