It's been known for some time that Public Folders are a deprecated Exchange Server feature, with Microsoft sounding the alert as long ago as 2007. As a result, Public Folders aren't available at all in Office 365 and Exchange Online, and unfortunately there's no simple migration path into SharePoint Online. Historically, such files needed to be migrated manually either into SharePoint or a local network file share.
Fortunately, today there are cost-effective tools to simplify this process. It is no longer necessary to first download files from Public Folders to the local file system, then re-organize and upload them into SharePoint Online. However, this is still a good opportunity to help you review the Public Folder structure, capture the business needs, and move into the new system in a way that provides the best value to you going forward.