Which distinction between ṣaḥīḥ li-ghayrihi and ḥasan li-ghayrihi is correct?

Innovation, Defective Retention, Ikhtilāṭ and Ḥasan li-Ghayrihi

• Both are necessarily fabricated reports
• They differ only in a narrator’s name
• Ḥasan li-ghayrihi is necessarily mutawātir
• Ṣaḥīḥ li-ghayrihi strengthens a ḥasan li-dhātihi report, whereas ḥasan li-ghayrihi elevates a mildly weak report