I found the solution. The Sata cable was the problem. I did exchange it and now both SSDs can be detected without any problem and in AHCI mode. Strange is that the HDD did work with the old cable but both SSDs not.  Resetting the Bios was another thing i tried before ordering a new cable - however this also didnt work.
Dear all, i upgraded my XPS 15 9560 with an Samsung M.2 970 Evo Plus 2TB NVMe SSD. That worked well, including the change from RAID to AHCI mode. Then i tried to exchange the old standard 1TB  SATA HD (HGST) with an SSD. I first installed a Samsung EVO 870 2TB and then later a Crucial MX500 2TB. Both are not recognized by the Laptop. I cant see them, neither in the BIOS (how should it look there?) nor in Windows. According to the Crucial website the MX500 should be compatible with the XPS. What can i do to fix the issue? Anything i have to take care of in the BIOS? By the way - BIOS and drivers are all up to date. Windows 10, Prof. 64 bit is installed. Thank you!
XPS 15 9560 doesnt recognize Samsung EVO 870 2TB and Crucial MX500 2TB