@Timelord64 Your answer is absolutely right, and I marked it as the chosen answer. But I want to add information.

In the PS3 Super Slim (my case) there's a thing that might confuse the user. When you insert the same hdd after removing it, the console asks you two questions: if you want to change the storage location to the hdd, and if you want to move the internal flash data to the hdd. 
Well, you have to answer yes to the first question and no to the second. Logical. But I though that by answering no to the second, I would not be able to do what I wanted. Glad it worked, and at the end, I got all data.