Anytime, even now.
After synchronisation Bitcoin Core should display updated balance, transactions etc. And then it will be possible to move coins to other wallet.
But there is also other solution: without waiting for full synchronisation (download of full blockchain) you my try to dump private keys and import them into other, maybe more user friendly client, like Electrum.
Google for command ’dumpprivkeys’, you need to do something like:
https://bitcoin.stackexchange.com/a/5933I have the original backed up on a different computer, will this suffice or do I have to back it up on the device I am currently syncing on? Also, I watched a couple tutorials on how to back it up and I am seeing people using "back up" from Bitcoin Core to achieve this. Is there another method to back it up?
Cheers!