Option 1: The President is authorised to transfer the Judge of one High Court to another High Court. This means that the President has the power to move a judge from one High Court to another High Court, based on certain circumstances or requirements.

Option 2: The Chief Justice of India does not have the authority to transfer judges between High Courts. The Chief Justice of India is responsible for the administration and allocation of cases in the Supreme Court, but not the transfer of judges between High Courts.

Option 3: A Collegium of Judges of the Supreme Court also does not have the authority to transfer judges between High Courts. The Collegium system is responsible for the appointment and transfer of judges within the Supreme Court and High Courts, but not the transfer of judges between High Courts.

Option 4: The Law Minister also does not have the authority to transfer judges between High Courts. The Law Minister`s role is primarily related to legislative matters and legal policy, not the transfer of judges.

Therefore, the correct answer is Option 1: The President.