Using the customer.updated webhook, you can have Bizplay send the latest customer and customer contact details to your administration system. You do have to make sure that the customer's Invoicing contact id in Bizplay contains the ID of the corresponding record in your administration system, otherwise the webhook won't be triggered.
Note that a customer can freely update his company details, regardless if the customer.updated webhook is active. So for minimal administrative effort, we recommend to use the customer.updated webhook as much as possible.
If you don't use the customer.updated webhook, you need to manually update the details in both systems.