Is it permissible to go to a city where there is no mosque, which would lead to missing Friday prayers for four months?

Your brother must leave the abode of the disbelievers and return to the lands of Islam unless there is a necessity or an overriding benefit. If he resides in a country where Jumu'ah (Friday prayer) is not established, he must pray Dhuhr. If there is a group of Muslims, they must establish the Jumu'ah prayer even if there is no mosque. If the required number is not available, then he should pray Dhuhr.