You can copy files like these to the current Firefox profile folder to recover specific data.

• bookmarks and history: places.sqlite
• bookmark backups: JSON backups in the bookmarkbackups folder
• SQLite files like cookies.sqlite (cookies) and formhistory.sqlite (saved form data)
• logins.json and key3.db (decryption key) for Passwords saved in the Password Manager
• cert8.db and possibly cert_override.txt for (intermediate) certificates stored in the Certificate Manager
• persdict.dat for words you added to the spelling checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other Site Preferences
• sessionstore.js for open tabs and pinned tabs and tab groups

You can use this button to go to the current Firefox profile folder:

• Help -> Troubleshooting Information -> Profile Directory:
  Windows: Show Folder; Linux: Open Directory; Mac: Show in Finder
• http://kb.mozillazine.org/Profile_folder_-_Firefox

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

it worked for the history and the bookmarks and cookies. thank you. the download list appears, but the folders are empty, and i understand why. is there any easy way to fix the directory somehow and make those download links magically work again? (again, my entire computer was wiped out ,and i did a data recovery which i put on to the new computer) also, my saved passwords seemed to not have been transferred over. any suggestion there? thank you

also, id like to move over the add-ons. and i cant find my old session restores either. and where is the recently deleted tabs icon on this firefox?

You only copy the download list (folder) that is stored in the places.sqlite. This doesn't of course include the actual files as stored on the hard drive. You would have to copy these files as well to the new computer if you want to keep them the same as with other personal data that you want on the new computer.

It might be convenient to resurrect your entire old profile on your new system. This would allow you to grab screenshots or copy/paste for easier comparison as you build your new profile.

This thread has the steps, although I haven't updated them for a while:

https://support.mozilla.org/questions/1111167