Let's take care of your reconciliation issues, vaolivas051909.
When your client converted their data from QuickBooks Desktop to QuickBooks Online, the reconciliation reports are not included. Hence, you'll see reconciled transactions showing as Reconciled (R) in your QBO register. This is part of the limitations when converting your data.
You mentioned that your client provided you the bank statements for 2013 and later. We can start correcting your data from 2013 and reconciling the following years: Reconcile an account in QuickBooks Online.
When reconciling year 2013, I'd recommend checking out this article to review the opening balances and your registers: Fix issues the first time you reconcile an account in QuickBooks Online.
Once you've reconciled that year, we can proceed to another year with ease. You might also find this link helpful if you encounter issues when reconciling the following year: Fix issues for accounts you've reconciled in the past in QuickBooks Online.
We got your back if you have additional queries regarding the process. Have a great day!