Notes

I tried to install Microsoft Office 2016 on a computer with a preinstalled evaluation version of Office. The installation was successful and I was able to activate it, but on every start the activation window popped up and I was not able to close it.

On the first time this happened, I tried to remove all remains of Office using the uninstall tool, but it didn't work.
After doing some research, I found some forum posts stating that I have to remove all oncurrences of a certain ID from the registry. This did the trick.

Unfortunately, I didn't note down what registry keys I had to remove. When this happened on another computer, I did not find the forum post again. Fortunately, I found another post in a Microsoft forum. As it turns out, all you have to do is to delete the following registry key:

HKLM\SOFTWARE\Wow6432Node\Microsoft\Office\16.0\Common\OEM

This worked perfectly for me. The activation window didn't pop up again.