If the object is animated, then you must have a common root object that everything else is attached to, it can be a mesh, or it can be something like a dummy object, but everything must be attached to it or they will be separated. When importing, make sure it’s set to import as a skeletal mesh, and that you check the box Import Rigid Animations
If it’s not animated, you can import as a static mesh, make sure to check the box Combine Meshes