If these are the same type systems, copy what you want to a thumb drive.

If it's just a small bit of information, you can send yourself an e-mail containing what you want. Note: If you want to send links, use the HTML and NOT plain text.

You can copy files from one profile folder on a different computer to your current profile folder to recover/transfer specific personal data.

• bookmarks and history: places.sqlite
• bookmark backups: compressed .jsonlz4 backups in the bookmarkbackups folder
• cookies.sqlite for the cookies
• formhistory.sqlite for 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

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

See also:

• 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