Hello? Is anyone there?

You would need ta previous copy of the places.sqlite file that stores the bookmarks and the history.

• https://support.mozilla.org/kb/Recovering+important+data+from+an+old+profile
• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox
• http://kb.mozillazine.org/Profile_folder_-_Firefox

@ cor-el: again, I've looked at those articles & they don't tell me HOW to actually OPEN the file. Could you please tell something helpful in terms of how to actually open it?

You can't open this file.
It is an SQLite database file that consists of multiple tables and records.
The file is in binary format and not very human readable.

The SQLite Manager extension or an external SQLite manger (sqlite3.exe) can show the records, but doesn't know how to interlink the tables to represent the bookmarks and the history like you see it in the Firefox.Library.
Only the Firefox Library code knows how to present the content in a way that is understandable and to be able to achieve this the file needs to be in the Firefox profile folder.

See also:

• http://www.nirsoft.net/utils/mozilla_history_view.html

Ok, so let my try to understand what you're saying: -the SQLITE file (in my Mozilla profile) CAN NOT be opened -in order to see the contents of the file (which are in binary), I have to have the SQLite Manager extension or an external SQLite manger (sqlite3.exe). Is this correct? If it is, could you please explain the rest of what you said in a way that I can understand?

@ cor-el: Hello? Could you please respond to my above comment?

I'm still seeing no need to inspect the places.sqlite file with other software as it isn't easy to understand if any data is recoverable. If you do not see the History in the History Manager (Library) when you place the file in the Firefox profile folder and make sure to remove all other places files then it is likely that this history data is lost.