Can you file a complaint in case of delayed delivery?

Hello,

On June 24, my mother ordered something from a store, but the package never arrived. As you can see in the image below, my mother can't track the package either.

After she first complained to DHL and inquired, they told her she would have to contact the sender, as only they could submit a tracking request. After she contacted the store, a tracking request was submitted.

Now, a month later, DHL demanded that we provide proof that no package arrived. We did this, it was accepted, and they are continuing to search and investigate.

My question is… You can file a complaint about a delayed delivery. Does that work in this case, too? Does my mother have to wait until the package shows up or until it's declared lost? Because we don't know who's to blame yet: DHL or the store. It's a large discount chain in Germany…

Can you request a reduction in the amount?

THANKS IN ADVANCE^^