Anyone using French Delivengo to ship MFN orders?

I am using French Delivengo (a service of french La Poste) shipping to ship Seller Fulfilled orders.

What Carrier and Delivery Service to you pick from Manager MFN orders? Do you enter La Poste (the originating Carrier), or the national post of Delivery country (Royal Mail, Deustche Post, etc.)?

The problem is once the package leaves France, it is delivered by the national post of the Recipients’ country. For example, I ship from France to a German address, the package ships via French la Poste and once it arrives in Germany, gets delivered by Deutsche Post, or if the order is going to UK, it will be delivered by Royal Mail. The tracking number stays the same.

It becomes a problem when a customer tries to track it via La Poste, the tracking number no longer exists once it leaves France. Or if I enter Deustche Post, it looks like the order was sent late, as the tracking number gets registered with Deustche Poste only once it arrives in Germany.

Is becomes a problem with proving A-Z claims when I need to prove that the package was delivered or shipped on time, Order defects, Feedback, customer messages inquiring about tracking, among others