public function __construct() {
    // "Test1" it's a title
    // FakeInventorySize::LARGE_CHEST is a size of FakeInventory (for small chest just type FakeInventorySize::SMALL_CHEST)
    // The "true" at the end is whether the FakeInventory should appear behind the player
    
    parent::__construct("Test1", FakeInventorySize::LARGE_CHEST, true);
}

public function setItems() : void {
    //$this->setItem(slot, item);
    $this->setItem(0, VanillaItems::DIAMOND());
}

// $player - Player which cliekd on item
// $sourceItem - It's the item that was clicked
// $targetItem - It's the item that was clicked (almost useless)
// $slot - It's a slot which was clicked by player
public function onTransaction(Player $player, Item $sourceItem, Item $targetItem, int $slot) : bool {
    // returned value means whether transaction is cancelled or not
    // example if return value is true then transaction is cancelled otherwise not
    return true;
}

$this->changeInventory($player, (new YourFakeInventory($player)));

$this->closeFor($player);

//if you want to open an inventory from a command level or another class, use
(new YourFakeInventory($player))->openFor([$player]);

//otherwise use this
$this->openFor([$player]);

$this->unClickItem($player);

<?php

declare(strict_types=1);

namespace your\namespace;

use fakeinventory\inventories\FakeInventory;
use pocketmine\item\Item;
use pocketmine\item\ItemIds;
use pocketmine\item\VanillaItems;
use pocketmine\player\Player;

class ExampleInventory extends FakeInventory {

    public function __construct() {
        parent::__construct("Second inventory");
    }

    public function setItems() : void {
        $this->setItem(0, VanillaItems::GOLD_INGOT());
    }

    public function onTransaction(Player $player, Item $sourceItem, Item $targetItem, int $slot) : bool {
        if($sourceItem->getId() === ItemIds::GOLD_INGOT) {
            $this->changeInventory($player, new YourInventory());
        }

        return true;
    }
}