According to the Constitution of India, the authority to transfer a Judge of the High Court to another High Court lies with the President of India. This power is granted to the President under Article 222 of the Constitution. The President is the head of the executive branch of government, and has the power to make appointments and transfers of judges in the higher judiciary. The Chief Justice of India, mentioned in option 1, is the highest-ranking judge in the country, but does not have the authority to transfer judges. The Speaker of the Lok Sabha, mentioned in option 2, is responsible for presiding over the meetings of the Lok Sabha and maintaining discipline, and does not have any authority in the transfer of judges. The Prime Minister of India, mentioned in option 4, is the head of the government, and does not have the power to transfer judges either. Therefore, the correct answer is option 3.