Hello Christen
You probably talk about the ZugerPass which allows, depending on the type, free travel within the canton of Zug.
It is only valid within the Tarifverbund Zug fare network and not beyond - neither fully nor partially.
If your son is aged 6-15.99 he can travel at half fare on any public transport vehicle in Switzerland. Is your son aged 16+, he needs a Half Fare Card (yearly subscription at CHF 185) to do so.
Kindly yours,
Roland