I'm Lucy, and I'd be happy to answer your questions today.
Unfortunately, no, you cannot. A court order issued in Wyoming is only valid in Wyoming. Most small claims courts do not allow people to sue non-residents for this reason. You CAN hire a process server in Texas to deliver the paperwork, or you can mail them to the person, but if they choose not to appear, there is no recourse.
What you can do is sue them in Small Claims Court in Texas. Before you go through the time and energy of doing that, you should know that Texas is one of the most difficult states to enforce a judgment in, because they don't allow wage garnishment. But if the person has any assets in Wyoming, you could go after those assets.
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