He would be eligible to go to public school but the majority of these schools teach in Swedish only. A private international school would likely be a better option, but fees can be exorbitantly priced. Some companies may be willing to provide a stipend for schooling, though, which may be something worth negotiating for in a relocation package. There are also a few other options for schooling that may be worth looking into. For more information, see our Education and Schools in Stockholm page.
Best of luck.
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