Step One: We first need to grab the Firefox profile off the old computer or hard drive. On the old computer, browse to (Windows XP) C:\Documents and Settings\\Application Data\Mozilla\Firefox\Profiles; (Windows 7,8, 8.1) C:\Users\\AppData\Roaming\Mozilla\Firefox\Profiles. You will find under the Profiles folder a xxxxxx.default profile.
Copy the Firefox profile folder to a flash drive or network location.
Step Two: Go to your new computer. Install Mozilla Firefox. If you are running Windows 7 or 8/8.1 go to C:\Users\\AppData\Roaming\Mozilla\Firefox\Profiles. Under the Profiles folder you will find a profile name (normally a string of numbers and letters with .default at the end).
Make sure Firefox is closed and cut the new Firefox xxxxxxx.default folder to your desktop.
Step Three: Ensure Firefox is closed on the new computer. Get your flash drive and copy the Firefox profile from the old computer into the C:\Users\\AppData\Roaming\Mozilla\Firefox\Profiles (Windows 7, 8 or 8.1) folder on the new computer.
Step Four: Go to your desktop and copy the name of the new computer’s Firefox profile. Next, go back to the profile folder (C:\Users\\AppData\Roaming\Mozilla\Firefox\Profiles) on the new computer, and rename the old computer’s Firefox profile to the exact same name of the new computer’s Firefox profile. In my case, I would rename the new Firefox profile (35jar636.default ) to H9gzaar6.default .
Open Mozilla Firefox and everything will be there just like your old profile. I hope this helps you. Thanks.
Source: http://techspeeder.com/2014/11/12/how-to-manually-move-your-mozilla-firefox-profile-from-one-computer-to-another/