What is the correct ruling regarding Friday prayer for two individuals who are traveling for the purpose of studying for four months, and have not found a nearby mosque, and one of them advised them to pray Dhuhr instead of Jumu'ah?

Since you have intended to stay for more than four days, you have become residents, and Jumu'ah (Friday prayer) becomes obligatory upon you if its conditions are met and it is established in this country. You must strive to search for the mosque where Jumu'ah is held. If you are unable to reach a mosque after searching, Jumu'ah is no longer obligatory upon you, and you must pray Dhuhr (noon prayer). You are not required to travel to another distant country.