You cannot copy/move posted time from one customer/project to another customer/project in Adagio Time&Billing. If you want to have the correct AR customer be used for information and created AR invoice batches, you have to remove the wrong information in Time&Billing and re-post it to the correct customer.

1) Create a project for the correct customer in Time&Billing.
2) Print a Time&Disbursement Ledger report for the wrong customer/project to get a list of all outstanding time and disbursements, yet to be billed.
3) Create a Time/Disbursement batch and enter all the transactions and hours/amounts appearing on the report in step 2, but use Reverse Time or Reverse Disbursement as the transaction type.
4) Before posting the batch from step 3, copy the batch and create a new batch. Change the customer/project codes to use the correct ones, not the old ones. Also change the transaction type from Reverse kinds to the usual Time or Disbursement.
5) Post both batches. The WIP for the incorrect customer/project should be cleared to zero, and the WIP for the correct customer is available for billing.

In Receivables, you could take the retrieved batch and edit the customer code to the correct one, but once batches have been posted, it's too late to make changes. You'd have to apply credit notes to improperly posted invoices in AR, and re-enter correct ones.