Zombies are not picking up diamond

Thank you for the correction. I hope they will fix the bug.

its very rare for a zombie to pick up items, keep trying and maybe you'll get there

I have tried even with a zombie spawner. Non of them picked up the diamonds.

This issue is not a bug, but a missing feature. It is not in the game source code to allow it to pick up items off the floor. However it may use items that are dispensed into it or using /replaceitem command. You should go to the feedback site if you want to request for this feature to be added to the game.

Zombies or any mob that can hold items do not have the CanPickUpLoot tag.

Thank you for your report!
However, this issue has been closed as Invalid.

We're already working on achieving parity across versions where possible, and we're very keen to hear your requests or suggestions, so we'd encourage you to make a post at https://feedback.minecraft.net, or upvote an existing topic there.

If you're not sure whether your issue is a parity request or a bug, hopefully this article will help explain further: Parity Request Guide

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@Sergiu Moldovan I believe that you are meant to get that achievement in multiplayer by throwing diamonds to another player. Recently when someone asked how to keep a hostile mob from despawning, others responded that they should get it to hold an item. Of course this is not possible in bedrock. Instead, they just need to keep it in the dark where it can't cross chunk boundaries and it will never despawn. So the mechanic of holding an item isn't strictly necessary, but you would think that they would at least pick up weapons and armor, which drastically changes gameplay.