So it was the "Ultra HD Switch 3 Port". The device promised to switch the inputs automatically, depending on where a signal is present. And it works flawlessly. The switch is hidden behind the TV and there inconspicuously performed his service. Perfect.
It is supplied with a small remote control, with which the inputs can also be switched manually. That would be the case if two devices simultaneously. An example would be if the cable box takes a picture while the BR player or Fire TV is used.
A power supply is included. What is very good, because HDMI is not USB, HDMI is therefore not intended to provide any connected devices with power. Switches of this type without power supply can even damage the electronics of the HDMI connection!