HI, you can transfer files from a previously used profile to the new profile, but be cautious not to copy corrupted files to avoid carrying over the problem. Never work with original files.

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

You should not rely on that to always happen and that folder to be created always :

• https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles
• https://support.mozilla.org/en-US/kb/export-firefox-bookmarks-to-backup-or-transfer

Please let us know if this solved your issue or if need further assistance.

For the passwords you need to transfer logins.json and key4.db. Note that key3.db has been used previously. You can use the button on the "Help -> Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page.

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

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

• bookmarks and history: places.sqlite
• bookmark backups: compressed .jsonlz4 JSON backups in the bookmarkbackups folder
• cookies.sqlite for the Cookies
• formhistory.sqlite for saved autocomplete Form Data
• logins.json (passwords) and key4.db (58+) or key3.db (57 and older) (decryption key) for Passwords saved in the Password Manager
  if you only have key3.db then make sure to remove an existing key4.db
• cert9.db (58+) or cert8.db (57 and older) for (intermediate) certificates stored in the Certificate Manager
  if you only have cert8.db then make sure to remove an existing cert9.db
• persdict.dat for words you added to the spelling checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other website specific data (Site Preferences)
• sessionstore.jsonlz4 for open tabs and pinned tabs (see also the sessionstore-backups folder)