1 - Download this plugin

2 - UnZip and upload folder my_plugin to /mod

3 - Don't activate this plugin yet.

4 - Copy file from

\vendor\elgg\elgg\views\default\entity\edit\icon.php

to 

\mod\my_plugin\views\default\entity\edit\icon.php

(Create non-existent folders)

5 - Open icon.php and change code on:

<?php


$entity = elgg_extract('entity', $vars);

if ($entity instanceof ElggEntity) {
   $vars['entity_type'] = elgg_extract('entity_type', $vars, $entity->getType());
   $vars['entity_subtype'] = elgg_extract('entity_subtype', $vars, $entity->getSubtype());
}


// custom code
if ($entity instanceof \ElggUser || $entity instanceof \ElggGroup) {
   $vars['cropper_aspect_ratio_size'] = false;
}

$content = elgg_view('entity/edit/icon/file', $vars);
$content .= elgg_view('entity/edit/icon/crop', $vars);
$content .= elgg_view('entity/edit/icon/thumb', $vars);
$content .= elgg_view('entity/edit/icon/remove', $vars);

echo elgg_format_element('div', ['class' => 'elgg-entity-edit-icon-wrapper'], $content);

Thank you very much for your help, really.

I can now crop it as I want, but when it is displayed on the profile, it is still square and not the cropped image in a rectangle.Could you tell me why?

By default, Elgg config has these sizes for avatars:

'icon_sizes' => [
   'topbar' => ['w' => 16, 'h' => 16, 'square' => true, 'upscale' => true],
   'tiny' => ['w' => 25, 'h' => 25, 'square' => true, 'upscale' => true],
   'small' => ['w' => 40, 'h' => 40, 'square' => true, 'upscale' => true],
   'medium' => ['w' => 100, 'h' => 100, 'square' => true, 'upscale' => true],
   'large' => ['w' => 200, 'h' => 200, 'square' => true, 'upscale' => true],
   'master' => ['w' => 10240, 'h' => 10240, 'square' => false, 'upscale' => false, 'crop' => false],
],

You can override this config via custom plugin.

Use My plugin again.

1 - Open elgg-plugin.php and add this code before last ];

'events' => [
    'entity:icon:sizes' => [
        'group' => [
           \MyPlugin\SetIconSizes::class => [],
        ],
   
        'user' => [
          \MyPlugin\SetIconSizes::class => [],
        ],
      ],
],