I got one of those years ago and never replied. Never heard back again.
A friend got one some time after that. He got scared and got a lawyer. He phrased a response letter with a reduced payment. He explained to me, that the phrasing is very important. You cannot under any circumstance show guilt for the alleged infringement, because then they come back with a vengeance (demands in the thousands of €). Paying the 900€ would already equate an admission of guilt.
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I’m not from Germany and not a lawyer so take this with a pinch of salt, but they wouldn’t be offering a settlement at such an early stage if they were confident they could successfully sue you. If it were me, I’d ignore them, and if it gets to the point I can no longer ignore them, I’d deny deny deny.
The situation in Germany is terrible - https://blog.raychenon.com/file-sharing-violations-in-germany/
In Germany private law firms can carry out the investigation, warning letters and prosecution, maybe in the latter case with the GVU. Germany loves its citizens reporting eachother ever since the DDR days.
My advice would be to move anywhere but Germany.