No, the payment cannot be transferred from booking to another booking. You would need to delete the payment in the original booking and add a new payment in the new booking. We do not recommend doing this as a better option is to Move rooms.
If you have received the payment via DPS, the payment is linked to the Reservation number, therefore by deleting it, you would lose the connection between DPS and the booking. A better option is to Move rooms with the payment.