I have been using Win 8.1 with Word 2013 and Zotero successfully for years. I switched to Office 365 (with a full version of Word 2016) on my Win 8.1. The Zotero.dotm is in Word, the Zotero tab with all the icons appears in Word, etc. but the macro will not function. I click on the icon, the screen flashes and nothing happens in Word. I am with adomasven in that the .dotm file is not working in Word 2016. I believe it is a permissions or macro security issue but cannot figure out what the actual issue is. I have followed all the instructions. The right files have been installed so it is not that. Your help is appreciated.
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If that doesn't help, see https://www.zotero.org/support/word_processor_plugin_troubleshooting#communication_error_or_non-responsive_plugin_buttons and, if you're still having trouble, let us know exactly what you've tried and what happened at each step.