You can do this by posting a refund (a negative payment) onto the old Booking/Invoice you wish to move it from, and then adding a Payment to the other Booking/Invoice.

We recommend adding notes so you are aware of what each transaction was for (something like the below image) or alternatively creating a specific Payment Type to keep track of these types of transfers.

Since Event Temple doesn't physically take any payments/refunds, you are merely just posting the money elsewhere in Event Temple - the guest won't see any transactions from their end regardless of which Payment Type you select.