When I process a layby in the Control Panel it does not say when I close the register at the end of the day.
The payment won't show on the register as you've processed the payment through the control panel, not the register.
The supported workflow for layby is to process the payments in POS, so then it syncs to the control panel.
This guide has more info: https://www.netohq.com/support/s/article/Layby
