No, since that can be easily falsified, but you've got nothing to lose by offering them the chat logs.
Generally, PayPal needs evidence of what the agreed-upon work was and that it was delivered. Invoices provide the former since they're supposed to include a description of the work, and you can prove the latter by showing PayPal the work during the dispute process. By comparing it with the invoice, they can see that you did deliver the work. If there's no invoice in PayPal's system, PayPal has no reliable evidence that the work you did is what the client agreed to.
This sort of situation is why invoices and contracts are so important. If you don't have a signed contract or an invoice that the payment is attached to, there's very little you can do, and PayPal will tend to take the customer's side.
is there any guide for invoices , i never heard of it before, ?
and you mentioned to check if the client has verfied paypal account, how do i check this after client send payments?