Yes, docuWeaver does support this. Using the Migrate to docuWeaver Apex action, you can build automation with Salesforce Flow to migrate your Salesforce files not only to SharePoint, but also to Amazon S3, Azure, Google Drive, and an external Salesforce org through docuWeaver.
Note: Migration of Salesforce Files depends on the heap size limits provided by Salesforce. Although Salesforce provides a standard heap size 12 MB limit for migrations, files that are close to this limit cannot be migrated reliably because other Salesforce processes also consume a significant portion of heap memory due to governor limits.
Additionally, there are file size limitations based on the storage server being used, as each storage provider processes files differently and consumes heap memory accordingly. For example, when migrating files to Amazon S3, files up to 8-9 MB per file can typically be migrated. However, this limit may vary depending on the storage server in use.
For more information on how to configure this, please refer to the link.