Who is the president to write a letter to if heshe is unable to discharge powers?

The process is governed under the United States Code, 3 USC 20 to be precise. A resignation is submitted, in writing, to the office of the Secretary of State, it takes effect immediately upon its receipt (for instance, when Richard Nixon resigned, Secretary of State Henry Kissinger initialed the resignation letter and noted “11:35” as its time of receipt), and it’s not subject to acceptance by anyone.