If, later on, he tries to get a one year extension of his OA visa he is going to need qualifying insurance. The insurance companies on this website qualify
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The insurance he uses to get his OA in the US probably will not qualify.
I discontinued my US insurance and bought Thai insurance.
I had an OA for 6 years. If he is OK about the insurance requirement then any time after the first year he can extend his OA for 1 year at a time without leaving Thailand. However, he has to check whether the insurance he uses to get the visa in the US will qualify for a 1 year extension inside Thailand. Probably not. The insurance required inside Thailand should be considered when choosing between an O and OA visa.
I had to do it for extensions of my OA visa. My point is that if something is easy and costs nothing then just do it. If immigration wants it they will ask for it or just give it to them and if they don’t want it they will hand it back to you. Worry about something important.
I posted about this about 2 weeks ago. In my case my passport was out of date so I had them update my account. It used to be that you didn't need a passport to buy a Rabbit card. Then they added the passport requirement and at the time I heard it had something to do with deterring money laundering. With all the concern with bank accounts these days it may be an issue with Rabbit as well. The BTS operators couldn't update my passport so I went to the Rabbit Card Service Center at the Phaya Thai BTS station.