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This is Jonis from Microsoft Online SharePoint Support.
The most effective way to print in SharePoint Online for Office 365 is to use a Web App to print from the browser. The links below detail Word and Excel printing through a Web App.
Introduction to Word Web App
Print an Excel workbook from the browser
If that does not answer your question or you are using a file that is not compatible with this solution, please let me know as I will continue to monitor this thread for any additional posts or questions.
Microsoft Office 365 SharePoint Support