optimize/simplify two functions (changeLetterNumber and registerMovements) with javascript

we are developing a chess game with javascript and I have been told to reduce/optimize/simplify the two functions that record the movements of the pieces (they are the two below), that is, reduce the lines of code as much as possible.
Everything works fine, all the pieces move, kill…
He creado también una tabla HTML que registra estos movimentos, movimiento realizado de cada pieza hecho por el usuario.
Thanks

function changeLetterNumber(box){
var row = box.substring(1,3);
var col = box.substring(0,1);
switch(col){
    case "1":
        return "a"+row;
    case "2":
        return "b"+row;
    case "3":
        return "c"+row;
    case "4":
        return "d"+row;
    case "5":
        return "e"+row;
    case "6":
        return "f"+row;
    case "7":
        return "g"+row;
    case "8":
        return "h"+row;
}
registerMovements(box);
}

function registerMovements(box1,box2){
  let piece = document.getElementById(box1).innerHTML;
  let piece2 = document.getElementById(box2).innerHTML;
  let col = columna(box1);
  let row2 = box1.substring(1,3);
  let kill="";
  if(document.getElementById(box2).textContent!="" && 
  document.getElementById(box2).textContent!="·") {//es kill
    kill=changeLetterNumber(box1)+" x "+piece2;
  }
  switch (document.getElementById(box1).textContent) { 
  //"♙""♖""♗""♘""♕""♔"/"♟""♜""♝""♞""♛""♚"
    case "♙":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerWhiteMovement").innerHTML += row;
        break;

    case "♖":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerWhiteMovement").innerHTML += row;
        break;

    case "♗":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerWhiteMovement").innerHTML += row;
        break;

    case "♘":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerWhiteMovement").innerHTML += row;
        break;

    case "♕":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerWhiteMovement").innerHTML += row;
        break;

    case "♔":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerWhiteMovement").innerHTML += row;
        break;

    case "♟":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerBlackMovement").innerHTML += row;
        break;

    case "♜":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerBlackMovement").innerHTML += row;
        break;

    case "♝":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerBlackMovement").innerHTML += row;
        break;

    case "♞":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerBlackMovement").innerHTML += row;
        break;

    case "♛":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerBlackMovement").innerHTML += row;
        break;

    case "♚":
        var row = "<tr><td>"+piece+kill+changeLetterNumber(box2)+"</td></tr>";
        document.getElementById("registerBlackMovement").innerHTML += row;
        break;
    }
    }


    HTML
    <table border="1" id="register">
     <tr>
       <th colspan="4"><h1>Movements</h1></th>
     </tr>
     <tr>
       <td colspan="2" id="registerWhiteMovement">Blanc<br></td>
       <td colspan="2" id="registerBlackMovement">Negre<br></td>
     </tr>
   </table>