The first thing I do when am added as a member or owner of a SharePoint Online site is to follow the site:
This tiny little button plays a big role in making the moving of files between sites and the saving of files to sites much easier.
I describe in detail how following a site helps people save files directly to SharePoint Online from Microsoft Word and other Office Desktop Apps.
I plan to write another blog post about how following a site helps people move files between SharePoint Online sites in the near future (spoiler: it’s a similar reason to why people can’t see SPO sites in MS Word, you need to follow a site for it to appear in the list of sites.)