Just sign into sync on the new computer and watch the magic happen. see screenshot https://support.mozilla.org/en-US/kb/how-do-i-set-sync-my-computer https://support.mozilla.org/en-US/kb/how-do-i-choose-what-information-sync-firefox

No, I want to transfer/migrate my data (bookmarks,passwords,history) across two accounts (from current account s**@***.org.pk to a new account sa**@gmail.com)

Create a Firefox account You will need a Firefox account to enable sync. To create an account:

Click the menu button Fx89menuButton to open the menu panel. Click the Sign In button next to Sync and save data. The Firefox accounts sign-in page will open in a new tab. Enter your email and click Sign up or sign in. Create a password and enter your age (Why do we ask?) and click on Create account Take note of the email address and password you used: You'll need them to sign in. Choose what information to sync. (See How do I choose what information to sync on Firefox?) You will receive a confirmation email from Firefox with a 6-digit confirmation code. Use it to confirm your account. Once your account is confirmed, sync is enabled automatically.

@techguy150 totally irrelevent reply, please dont clutter my post

I am not a sync expert, but my thought would be to pick a device that has all the data that you wish to sync, sign out of the old account in Firefox on that device, then sign into the new Firefox account and set up sync for this account?

But whatever you do, backup your data locally before attempting this. For information on backing up your data see: https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles

Another possibility would be to create a new profile, manually copy your data locally from the old profile to the new, and then set up sync in the new profile with the new account. For information about which files to copy see: https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile#w_your-important-data-and-their-files

Personally I would try the latter first as it is probably a bit safer? But again, I do not claim to be an expert on sync.