[Alz007]

They asked me by phone call so no

In future, get a reference number for the phone conversation, as well as the full name of the person you spoke to.

Is it safe to fill out the affidavit?

It may only be required to move forward with the claim but given It's a legally binding document, I always suggest not to sign It.

Ultimately, It's your call.

I didn't think of that, I will next time. But technically they have the recordings of the conversation, right?

So concerning the certificate on the honor I managed to get from them a modification of it after several calls in which I explained that I had received the package and that the certificate on the honor was in the case I had not received the package (I do not want that it has a negative impact on the GLS deliverer, blah blah blah...). And they sent me back a new certificate on honor slightly modified in which it is marked that I did not have in the package received after checking my headphones and the charge box. Is it ok for me to fill in this certificate now that it has been slightly modified or do I still have to insist to the customer service that they recognize my EB?

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explained to customer service that the charge box and headphones were not in the package. They misunderstood me and thought the box was completely empty. Since then they have treated my request as a DNA

From what I've read in this thread after I posted my success story, it seems like this is the main source of troubles other people have encountered.
I must've been incredibly lucky to have gotten a rep who fully understood I was claiming MEB rather than DNA.
P.S. what does the affidavit say? Any mentions to it being legally-binding in any way or form?

Their communication is horrible, I don't know if they do it on purpose or if they don't understand but it's something...

The content of the two affidavits in terms of legality:
I have taken note of the provisions of article 441-7 of the penal code, repressing the establishment of a certificate stating materially inaccurate facts, hereafter recalled: "Is punishable by one year's imprisonment and a fine of 15,000 euros the fact of establishing a certificate stating materially inaccurate facts".

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Two more details: 1. I did not open the package properly, which could give the impression that the seal was torn off. Even though I explained to them that it arrived intact at my home, they kept telling me that the product had been put in the package when it left the warehouse and that since the seal had been ripped off, it must have been stolen by someone at GLS...
2. I managed a few days ago (before they saw the pictures of my package) to make them understand that it was indeed an EB and the rep told me (after consulting with his superior) that I didn't need to fill out an affidavit for that.

What should I do then? Fill out the affidavit and if it goes wrong pretend I didn't understand or call them again and again until I can talk to someone who understands my situation or escalate my request?

Excuse me @mothered, can you tell me what do you think about that please? And what do you think is the best solution ?