So, according to the description and the other reviews after I could not tell if I with a DVI output could with my new projector, the course only has HDMI ports connect my PC. Since the adapter cost only a few euros, I take a chance and lo and behold, it works. I have a DVI cable, which is connected to the PC. The other end I have connected to the adapter and the adapter to the projector (HDMI input). I had feared that eventually the adapter works only in one direction, ie that you can connect a new satellite receiver with HDMI port on an older monitor with a DVI port, for example (as was the description), but went the other way around it to luck also. Therefore, I can recommend this adapter to anyone who has the same boundary conditions.
PS: The signal quality I can not judge, and I have no problems with this. The signal is transmitted digitally anyway. Even with the 5 m cable plus adapter I see nothing negative. The adapter itself is to judge by my modest skills well finished.