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I believe he will need to show proof of having completed a hunter education course when he buys his license. So yes, the hunters ed card from Texas will work just fine, if he has one. He shouldn't have to go to Olympia. Any license dealer should be able to handle it.
Have him buy his small game Bear Lic NOW while he is still active Military... Then when if he wants to add anything its will be easy. Proper Preparation Prevents Piss Poor Performance!