JSFiddle - React, Tailwind, and code Playground

JavaScript

// your object
var o = {
    "numbers": [
        {"id":"11111"},
        {"id":"22222"}
    ],
    "letters": [
        {"id":"aaaaa"},
        {"id":"bbbbb"},
        {"id":"33333"}
    ]
};

// gets the index
// a = the array to look in
// p = the property to check
// v = the value to check
function getIndex(a, p, v) {
    for(var i=0; i < a.length; i++) {
        if(a[i][p] == v) {
            return i;
        }
    }
}

// get the index from the letters array with property 'id' with value '33333'
var index = getIndex(o['letters'], 'id', '33333');
console.log(index);
// if you found the item
if (index !== undefined) {
    // get the actual item from the array
    var item = o['letters'][index];
    console.log(o['letters']);
    console.log(o['numbers']);
    console.log(item);
    // add the item to the other numbers array
    o['numbers'].push(item);
    // remove the item from the letters array
    o['letters'].splice(index, 1);
    console.log(o['letters']);
    console.log(o['numbers']);
} else {
    console.log('did not find the item');
}