When an invoice is sent to Xero a link is created in Accelerate between the invoice payer (relationship/dealer/funder) and the contact in Xero that the invoice was assigned to. This link persists, so that the next time you send an invoice to Xero for that same payer you aren't prompted to select a contact each time. These links are stored within Settings > Xero Settings > Contact Links:
You do not need to manually create these links, but that option is available. If you click the 'Add Xero Contact Link' this will display a popup where you can select the invoice payer and the associated Xero contact.
Leaving the Xero Contact blank will automatically create a new Contact in Xero when you click the Save button. From this screen you can also change the Xero Contact that is associated with an invoice payer or remove the link completely. So if you have accidentally associated a payer with the wrong Xero Contact then you can correct it by editing the link record from this screen. You can also associate multiple payers with the same Xero Contact record if needed.
If you archive a Contact in Xero, then any links to that contact record in Accelerate will automatically be removed. And if you update the name of the Contact in Xero then this is reflected in this screen, however this link is only there to determine which contact record to associate and invoice with. So if you update the relationship/funder/dealer name in Accelerate, this does not update the Contact in Xero and vice versa.