Rated 5 out of 5 stars

Problem solved! See below!

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Sorry for using the rating for feedback. Just to say it: After the update I have the same problem with the request for cookies. Thus, the add-on does not work on my PC with Thunderbird 52.9.1, Provider for Google Calendar 4.4.1.

Updates:
Installed, Thunderbird 60.0, same problem.
Installed Provider for Google Calendar, older Version 4.4, same problem.

(The last PfGC version I could use was 3.3, but it is not declared to be compatible with TB 60.0. so I don't try it.)
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Problem solved in the options for Thunderbird:
Privacy -> enable Cookies for Websites
pref.privacy.disable_button.view_cookies -> true

This review is for a previous version of the add-on (4.4.1).