How to extend the built-in Array Type on Typescript with the extend method? Property 'foo' does not exist on type 'String'

For reference, I am using React 16.9.0 and Typescript 3.5.3.

On this question How to extend an existing JavaScript array with another array, without creating a new array, I found how to create the new method extend on the Array type:

Array.prototype.extend = function (other_array) {
    /* You should include a test to check whether other_array really is an array */
    other_array.forEach(function(v) {this.push(v)}, this);
}

But when I try to add Typescript support (for type checking the array type), I cannot find how to make it work. This is how I tried:

interface ExtendedArray< Type > extends Array< Type > {
  extend: () => void;
}

if( !( 'extend' in Array.prototype ) ) {
  Array.prototype.extend = function (other_array: ExtendedArray< any >) {
      other_array.forEach( function(element) { this.push( element ) }, this );
  }
}

Typescript just keep insisting my ExtendedArray type does not have the prototype.extend attribute:

Property 'extend' does not exist on type 'any[]'.  TS2339

    52 | if( !( 'extend' in Array.prototype ) ) {
  > 53 |   Array.prototype.extend = function (other_array: ExtendedArray< any >) {
       |                   ^
    54 |       other_array.forEach( function(element) { this.push( element ) }, this );
    55 |   }
    56 | }

After searching more, I fond this other question Extending functionality in TypeScript, with this example:

interface String {
    foo(): number;
}

String.prototype.foo= function() {
    return 0;
}

But if I try to run it, Typescript just strikes its rage:

Property 'foo' does not exist on type 'String'.  TS2339

    41 | }
    42 | 
  > 43 | String.prototype.foo= function() {
       |                  ^
    44 |     return 0;
    45 | }
    46 | 

How can I extend a Javascript builtin the prototype with a new function on Typescript?