Hey @GuillaumeLar ,
Unfortunately, I haven’t found a way to do this. Based on my usage and documentation of the Fulfillment and FulfillmentOrder APIs, this is not impossible. There are two fields on the Fulfillment called created_at and updated_at, but they are read-only (though the documentation does not mark them as such).
I haven’t heard from the Shopify team to confirm it, but I haven’t found a way to make it work, given the API resources.
If you end up finding a way, please let us know. 
Ralph