Thanks for the reply Kevin.
My question is not about the preparation work, but really about the migration itself. I am on Office 365 and I need to pull there the structure that existed on SharePoint 2010.
I think your link provides the answer (unfortunately not the one I was hoping for):
Office 365 does not provide SharePoint content migration support for customers. If you plan to migrate SharePoint content from an on-premises or hosted service to SharePoint Online, your organization will either use a manual approach or to use a third-party SharePoint migration tool.
I would be interested to know if there are any third-party SharePoint migration tools that are appropriate for a single site collection migration from a hosted SharePoint 2010 to Office 365.
Thanks,
Christophe