When you are on the old computer, let us know. You will have access to nothing from the old computer until you setup sync on the old computer and then repeat those steps on the new computer. Please don't be like so many user that get rid of the old computer and think your data was backed up via sync. Read this 20yr user issue who just lost all of his data because he thought sync was a back up service. https://support.mozilla.org/en-US/questions/1419930#answer-1594611 Keep both computers until you see your data on both computers!

If you don't have data (bookmarks and passwords) on your old computer, then there is no real issue.

You can copy certain files with Firefox closed from the old profile folder to the profile folder on the new device to transfer personal data. Note that best is to avoid restoring a full profile folder and only restore important files that are safe to restore/transfer.

You can use the button on the "Help -> More Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page (Root directory).

• Help -> More Troubleshooting Information -> Profile Folder/Directory:
  Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data
• C:\Users\<user>\AppData\Roaming\Mozilla\Firefox\Profiles\<profile>

• bookmarks and history: places.sqlite
• favicons: favicons.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 (encrypted logins) and key4.db (encryption key and primary password) for logins saved in the Password Manager
• cert9.db for certificates stored in the Certificate Manager
• persdict.dat for words added to the spell 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)