Can I transfer hosted services from one ArcGIS Online organization to another?

No, it is not possible to transfer content from one organization to another but you can copy/clone items using the ArcGIS API for Python. The hosted service itself can be cloned to a new ArcGIS Online organization. The process is outlined in this Knowledge Base Article: How To: Copy/clone hosted feature services (including data) from one ArcGIS Online organization to another