After that "someone" sent you the transaction ID and you can confirm that it has confirmations with blockexplorers (blockchain.info) it's in that wallet, assuming that the address belongs to it.
You can take all the time in the world before syncing/opening that wallet again.

If this actually happened back then, there's nothing else required to complete "that" transaction.
If the bitcoins isn't there after synchronization, either the transaction was dropped or it isn't the correct wallet.dat from 2010.