Sounds like you are already familiar with how to locate your old Firefox profile folder which contains your data from your previous installation of Firefox. The following article has the names of the two files needed to transfer your logins -- you'll want to copy both of them over while Firefox is closed so they replace the new empty ones.

• Recovering important data from an old profile

And just in case --

• Profiles - Where Firefox stores your bookmarks, passwords and other user data

Did it work?

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