hello vanaya2002, firefox sync was not primarily designed as a backup service but to keep multiple devices on the same level.

in order to access the data in your sync account you'd need three components: the username, the password & the recovery key generated during the original setup of the account.
in case you have all those three pieces of information available, you can go to firefox > options > sync > set-up sync > i have an account > i don't have the device with me in order to link firefox to your existing account.

You can only use pair a device if you have already setup Sync on another device because that is how pairing works: both devices need to be online and one connected to the Sync server.
Then you can enter the 3x4 character pairing code that the second device that you want to add supplies on the device that is connected.

Obviously you can't use this method if there is only one device and you need to enter all three parameters (account name, password, and Sync key) manually.

If you didn't backup the Sync key then you are out of luck and can't connect to the Sync account and access the previously stored data (Sync Options: Replace all data on this device with my Sync data).
Generating a new Sync key will remove all data that is stored on the Sync server.

Thanks for the quick replies. Too bad this didn't work for me this time.