Hi @fmonnot,
Thanks for reaching out. Eugene is right. If you're looking to update the online version using the same Publish Online URL, the document needs to be republished from the same Adobe ID that was used to publish it originally, and it must have the same file name.
Once your client has updated the InDesign file, you'll need to open the same file (with the same name) using the original account that published it. Then go to File > Publish Online, and instead of creating a new document, you should see an option to Update Existing Document. Select that, and your updates will be published to the same link.
Let us know if that works for you.
Abhishek