Step 1: done.
Step 2:the name of my new Zotero data directory is C:/Users/Braulio/AppData/Roaming/Mozilla/Firefox/Profiles/mcr0767v.default-1473507032293/zotero; it has a folder named "zotero". I kept this folder open and closed Firefox.
Step 3: I renamed file "zotero.sqlite" to "zotero.sqlite.old" and folder "storage" to "storage.old"
Step 4: the "Old Firefox Data" in my desktop has 2 folders: 1)nj5ty3mg.default and 2)v24fxcvh.default-1473271160084. In the first one there is a folder named "zotero"
Step 5: from "Old Zotero Data" (folder "zotero"), I copied the "zotero.sqlite.old" file and "storage.old" folder to the new Zotero data directory, that now has (among others files and folders): 1) folder "storage" and "storage.old" and 2) files "zotero.sqlite" and "zotero.sqlite.old"
Step 6: I restarted Firefox, but my library is not restored.
Which is the mistake I am making ?

Correction: in Step 5, I erroneously wrote "Old Zotero Data" instead of "Old Firefox Data".
The files I copied do have the .old extension. The size of zotero.sqlite is 1.188 MB.

By the way, what is the purpose of adding ".old" to the file "zotero.sqlite" and folder "storage" ? To have a backup of them ?

1)You said: " That's basically an empty library". What do you mean with "That" ? ¿zotero.sqlite ?
2) There is not a "zotero" folder/file in the other old profile.

The contents of the zotero folder within "Old Firefox Data" is:
Folders: locate/storage/storage.old/styles/translations
Files: pdfinfo (1 KB)/pdfinfo-Win32 (584KB)/pdfinfo-Win32.exe.version (1 KB)/pdfinfototext (1 KB)/pdfinfototext.Win32 (580 KB)/pdfinfototext-Win32.exe.version (1 KB)/zotero.sqlite.old (1128 KB)

I have changed the original name (zotero.sqlite) to zotero.sqlite.old.
My database has1130 items

Old Firefox data, on my desktop, has 2 folders:
1)nj5ty3mg.default, with 19 subfolders; one of them is "storage", that has 3 subfolders ("default" (with 8 subfolders), "permanent" (with 3 subfolders) and "temporary" (with 7 subfolders));
2)v24fxcvh.default-1473271160084, with 13 subfolders; one of them is "storage", with just one subfolder ("permanent" (with 2 subfolders))

I'm not quite following, but this

a zotero/storage subfolder with 1057 elements (or subfolders)

is correct. Those are your original Zotero attachment files as backed up by Firefox. So in the directory containing that 'storage' folder', there's not a zotero.sqlite* file that's larger than 1 MB?

OK, at this point, since you have your library online, I'd just sync:
https://www.zotero.org/support/sync
That shouldn't be necessary, but I'm not sure we'd be able to find the database on your harddisk still.
Make sure you can open attachments after syncing -- otherwise we'll be able to tell you how to fix that.

OK, copy the content of this:
zotero/storage subfolder with 1057 elements
into the storage folder that already exists in your current, active data directory, replacing existing files.

that's
C:/Users/Braulio/AppData/Roaming/Mozilla/Firefox/Profiles/mcr0767v.default-1473507032293/zotero/storage

I'm confused. Could you post a picture of what you're seeing on a free image hosting site and link to from here?
(Edit: just to clarify -- whether you have a 3-panel Zotero display or not has nothing to do with restoring your back-up. That's just a question of where/how you look at this -- hence my confusion).

I use Zotero on an older macbook and have 3 pane view in my Firefox browser. I find it a very useful way to work with Zotero.
Unfortunately when I installed Zotero on new macbook, I downloaded the recommended Zotero for Mac, and also the Zotero Firefox Connector thing.
Now, I am not able to see Zotero in the same way in the Firefox browser, and it's a poorer version in my opinion. Currently, if you save a citation from the browser into the standalone version it's a bit hit or miss if you save it into the correct library folder, etc.
Am I missing something in the set up on my new laptop? Is there a way to have the red 'Z' on the menu bar of Firefox browswer, and if it is clicked it opens up the Zotero interface, including libraries, in the lower part of the browser? I can mail a screenshot of the old set up if that helps.
Cheers

On the new, just like with Zotero 4, items are imported to the selected (open) collection within your library.

I think that it's a pity, and the user experience most certainly is degraded as a result

"most certainly" is a little strong — it's a perfectly reasonable perspective, but remember that Zotero Standalone has existed for many years, and many people prefer the separate app.

And frankly, it's not the case that the interface is the same as suggested below!

While I understand your point, I think it's pretty clear in context what that line means — it really is the same interface in a separate app, literally running off the same code. Zotero for Firefox and Zotero Standalone were designed to be interchangeable, and people often switched back and forth as they worked, with the same three-pane interface in both versions.

I think the changeover could have been more explicitly handled, I've wasted alot of time trying to figure out why Zotero wasn't working as before - including searching extensively on the Zotero website.

Sorry for the hassle. In our defense, this is explained in two of the three blog posts under "Zotero News" on the front page, and when you first run the Zotero Connector for Firefox and click the button there's a dialog that says this:

Looking for your Zotero data? If you were previously using Zotero for Firefox, you’ll need to download the standalone Zotero application to access your local Zotero data going forward. See A Unified Zotero Experience for more information.

And you have to click "Got it" to continue.

Maybe I might suggest that the news story should be linked to from the download page rather than two enormous download buttons.

We've added a prominent line to the top of the download page for Firefox users that links to the blog post.

We also haven't actually upgraded Zotero for Firefox users to the new version yet, so the change so far is limited to people manually installing the new version. We're going to try to push out another build of Zotero 4.0 for Firefox that gives a clear warning about the upcoming change when you open the Zotero pane.

OK, so it looks like you're new to these forums and perhaps to open-source software, so you should understand that this is a pretty friendly place where Zotero developers and community members spend a huge amount of time engaging with users and discussing together how to improve the software.

I engaged with your criticisms, provided the reasoning behind a line that you disagreed with, apologized for your wasted time, explained the fairly extensive steps we've taken to manage this difficult transition (including an explicit notification that you clicked through), told you that we've already adopted one of your suggestions, and explained some additional steps we're going to take to avoid further confusion. If "ROFL - Classic response" and snark seem like an appropriate response to that, there's really no need to post here.