Thank you for the explanation, but maybe you misunderstood me.

Those coins were sent in 1 chunk to my local wallet after many days of collecting micro payments on coinbox.me

The Bitcoins are already in my local connected wallet.
Now, since I have them in one wallet, I wanted to move them to another wallet to see how it works, just like moving regular money change coins from one pocket to another.

When I move physical coins from one place to another they don't lose on their denominated value and there is no fees.

In here I tried to move all I had: 0.00016519 BTC from one local wallet to another and they tried to charge me over 60% of my savings to do so just for 1 transaction.

I think that is ridiculous. These coins are already in the system and don't need to be mined any more.