How to send stream to server without any compression? How to send stream to server without any compression (output should be exactly the same as the video stream being sent)?

ffmpeg doesn't seem to be able to do that. It always lose something (based on filesize and ffprobe output). Is there any alternative?

This question is asking for alternative to ffmpeg that may do the job more easily than ffmpeg.
Any video you plan to stream from a host machine to another endpoint, or multiple endpoints, will have to be encoded. The question is what is your source? Are you streaming a live video feed? If so, in order to stream uncompressed you’d first have to have your capture setup to injest the video as an uncompressed format, 4:4:4. Even with just 1080, you are talking huge amounts of data. 

For uncompressed, to stream over the internet, youre going to need a serious rock solid network uplink... 1000mbps up or greater depending on the frame size.